trigonometry grade 10 maths cbse part 1

[00:00:00]See uh salt is left. Salt part is left.

[00:00:04]After salt what is left um salt salt section means AC bases and salt will get finished. Now we finished human and colorful world defects we have finished. Now we have prism internal reflection and prism that section because uh this see Understand?

[00:00:45]Good morning. Just sharing link.

[00:01:00]>> [clears throat] >> Everyone listen Sunday you are having AP test arithmetic progression test uh kundam students inform them today there is no mercy for them they have taken so much of rest so their work so I'm starting today. Huh? Because in har today is the 22nd or 23rd beta. Jerum, good morning.

[00:01:37]Shanmati see triangles and trigonometry both in trickle kundam session I will be teaching today's session. Don't miss about trigonometry. Okay? Because today evening I'm starting triangles morning trigonometry. I have no other ways.

[00:01:54]August you have three s two sample paper exams from coaching.

[00:01:59]Eight chapters are see eight chapters they're telling means seven marks I told you know corner geometry they are asking I can't leave that 11 marks trigonometry they are asking so I can't do that I can't say them no okay once commitment then means I have to finish evening similar triangles I'm teaching in trickle kundam morning I'm teaching here trinometry because gateway school also having you school also similar triangle they started so we have to go by both the ways okay so today evening I I will not say you do this do that today evening you people have to be present for similar triangle classes okay see please understand I'm doing this not for me for you people only so concept of similar triangle again I will teach you but today it is important trigonometry can I start see there are many triangles okay I starting the concepts of trigonometry see now there is a bigger good morning jer good morning rashan if today he's not attending classm he's in trouble rohit rashan and pineal. I think pineal is present. Kartik is present.

[00:03:03]Kartik, Shmati, Leita, Zerum and Tipika. These people are present. They are saved by me because today I'm going to seriously punch these people. Now look here.

[00:03:19]It will not take me 2 minutes to take some decisions. I told you now because study means study. Score means score.

[00:03:25]They will not say that how much intelligent you are. But you people have to work in your handwriting. One very bad news is coming. That bad news is many of the student they wrote retest in mathematics. Okay. They only increased one or two marks maximum five marks.

[00:03:41]They did not give more marks. No matter the student did good in exam they are very this paper they wrote very good only five marks or six marks. You need to understand EI correction means they will need clarity in your paper. First thing A should write like A not like B.

[00:03:59]Keep some distance between two letters.

[00:04:03]It should not merge with each other. If they will not understand, they'll not give much. Understood?

[00:04:09]Because they are now learning.

[00:04:13]Understood? Not the the mixing of words and all that things. No, it is not going to be awarded. Please understand that got it Amish your handwriting your presentation is lagging I want presentation work please everyone so now look here the opinion is not present I'll seriously punch these people get ready everybody so now understand in triangle there are different type of triangles now triangles will have sides and angles got it but there is no concept in mathematics which was able to teach that we can generate a relation between sides and angles. Sides and angles. When you were studying geometry, you were discussing about sides. Correct? Angles separately. Correct. Now sides are equal. This is there. That is there. But we there was no part in mathematics which were able to differentiate or relate sides and angles and because of that the concept of trigonometry came.

[00:05:10]Understood? So when trigonometry came it related sides and angle good morning.

[00:05:16]When trigonometry came everyone listen carefully amish good morning please. So sides and angles relation they have generated but what type of triangles you are needed? You need right angled triangle for trigonometry. What are type of triangles you are needing? Right angled triangle. Understood not now there are two type of right angle triangles.

[00:05:39]Two type of right angle triangles. Come on draw fast. Two type of right angle triangles.

[00:05:47]There are two type of kanesh. Good morning. There are two type of right angle triangle. Can who can explain me what are the two type of right angle triangle? This is one type right angle triangle. 90° confirm for right angle triangle. Yashika good morning everybody check you people are online or not. Yes Shanati. Right angle triangle are of two type. One right angle triangle is this what he has drawn. So right angle triangle will have hypotenus base and perpendicular. Done. Another type of right angle triangle.

[00:06:25]One type of right angle triangle.

[00:06:26]Everybody will draw disha present. Okay.

[00:06:30]Give me better. So this is a right angle triangle. Absolutely correct. One angle is 90°. Understood. So this is one type of right angle triangle. First basics.

[00:06:39]Yeah, good morning. So, see everybody please pay attention here. One type of triangle is right angle triangle. One type of triangle is isocles right angle triangle. Understood? No doubt. Right angle triangle is of two type. One is only right angle triangle where base hypotenus and side perpendicular all will be different. Understood? All will be different. That's absolutely correct.

[00:07:06]All will be different. Then it is called as what? Right angle triangle. But here right angle triangle is divided into two parts. This is right angle triangle.

[00:07:22]Right angle triangle. Another right angle triangle is this one. This is called as isocillus.

[00:07:38]This is called as isocelis right angle triangle. What it is called as beta?

[00:07:42]Isocelis right angle triangle. Everybody please be accountable for this. Isocelis right angle triangle means the perpendicular is equal to base.

[00:07:55]Perpendicular is equal to base. Means this side will be equal to this side. Because in isocles triangle two sides are equal. In isocles triangle what is there hash? Two sides are equal beta. Always remember here this in this perpendicular is not equal to base. This right angle triangle perpendicular is not equal to base. But here perpendicular is equal to base.

[00:08:18]Amish. Did you understood the difference between these two?

[00:08:22]Yes, there is a difference. Here perpendicular is not equal to base. Here perpendicular is equal to base zero.

[00:08:30]This is the biggest difference between an isocles triangle. See this is isocelis and right angle. Understood?

[00:08:37]And this is only right angle. Got it? So here there are two different type of triangles in one. That is isocelus also and right angle triangle also. Here this is only right angle triangle. Did you understood the difference? Please come on children start typing. Yes. If you have understood everybody understood. So what are the two different type of right angle triangle? The two different type of right angle triangles are right angle triangle only or right angled isocelles triangle understood isocelis right angle triangle very good everybody keep typing yes I'll understand that you people have understood now in right angle triangle for trigonometry you need to do one word everyone one shortcut technique I'm teaching you this shortcut technique will be always beneficial for you see you need to learn one thing whenever whenever Whenever you are taking right angle triangle now they told to find this angle relation six trigonometric ratios this angle.

[00:09:37]So whenever this angle and 90° will be there whenever they told to find this a b c six trigonometric ratios of angle a don't think too much this will become your base or adjacent.

[00:09:59]Understood? Hypotenus will never change because hypotenus is the longest side. Understood? Hypotenus is the longest side. It is not going to change.

[00:10:09]People please remember hypotenus is what? Longest side. We not going to change hypotenus. That what is exactly going to change? Always we will change perpendicular and base location. Which angle a see very nicely beta which angle you are taking with 90°. If these two are taken it will become a base and opposite one will become a perpendicular. Understood?

[00:10:34]This part will become perpendicular. And now what is the other name of perpendicular? Many people in NCERTT book this is called as opposite.

[00:10:44]And this one is hypo t n u s e.

[00:10:48]Hypotenus will never change. Understood.

[00:10:50]Hypotenus will never change. So this is the shortest way because many students now many many many many opposite side.

[00:10:58]Very good. Monish. Good morning beta.

[00:11:00]Mish. Can you inform Ilamar to join the session today? See, we don't have too much time. We have to study. Vetri, thank you so much for joining the session. Beta, I really feel thankful to you children. Please join as fast as possible. So, hypotenuse, perpendicular and base. So, look at this base is called as what? This part where you angle A and B you are taking together.

[00:11:23]So, this angle with perpendicular taken together by default it will become what?

[00:11:28]base and opposite side will become perpendicular this you have to remember understood or not now one story I'll tell you with the help of this yes absolutely adjacent super zero everybody please be present and mark your present and start writing now look here one small story I'll tell you there are six trigonometric ratios okay so in six trigonometric ratios three trigonometric ratios you are knowing miss remaining three you will do how many you have to three others you will do on your own.

[00:12:02]Understood? So now how they are related to each other and how they are going to solve it because we I will teaching you now typical questions of trigonometry this year six marks trigonometry they gave like that students were unable to move the question but our students because same pattern questions we did they solved and came are you understanding they solved and came what is the highest from our coaching this year maths 100 is the highest understood yes I got 100 online students And he was mad about classes.

[00:12:36]99 is sorry maths is 99 and science is 100 highest. Okay. So with this tough paper also our students got it. Correct now. So now let's go for it. We can do it.

[00:12:50]Ready?

[00:12:51]So please understand one thing. I'm ready. How many trigonometric ratios?

[00:12:56]>> Six trigonometric. So s we don't call it sin. We call it sign. Sin A. Okay. See if this angle you have to find this angle will correlate with the three sides. Okay. So sin A the total name is cosine sine cosine tangent. What is the full form? Sin cosine tangent. Online children in your home itself you speak sine cosine tangent. Again say sin cosine tangent.

[00:13:33]Online children please repeat in your home. Sin cosine tangent. Understood.

[00:13:39]Sin cosine tangent. But we are not writing full. We are writing only short sin cos tan. Understood? Sin cos tan because every time we cannot write the full name. Now once you are writing sign s reciprocal part will be there. Yes.

[00:13:58]No tan small. Many places they writing T capital. Many places they writing T small. But tan we are referring T small only. Okay. Now look here. Sin cosine tangent. Tangent. What it is called as?

[00:14:11]Tangent. Sin cosine tangent. Opposite of s is coseant but we write cos.

[00:14:21]Understood. Name is coseant.

[00:14:24]So I will be always speaking coseant.

[00:14:26]Cosecant means cos understood. Say this is called as seeant. Now I hope you might have understood. And this is called as tangent c.

[00:14:39]Got it. Who is opposite standing with sign >> s cos sin cos cos sec tan cot. You see the sound pronunciation. Sine cos cos sec tan cot sign >> cos >> 10 c that's it now how they are related see one story is there that is if you write perpendicular by hypotenus always remember hypotenus will be down for all the three now whenever you will be writing [laughter] No 75. So look here. So whenever you will be writing always remember one thing. Whenever you are writing hypotenus hypotenus will bend down.

[00:15:33]Understood for s and cos. So for sign you remember with this b h and this by this easy to remember p by b is that p by h b by h p by b. Is it easy to see that symmetric? P by H, B by H and P by B. P by H, B by H, P by B.

[00:16:00]Understood? P by H, B by H and P by B.

[00:16:05]Got it? Now opposite you. H by P, H by B and B by P. All sixometric over. That's it. Note down please understood. I'll make trigonometry like dance for you. Whatever you will do in trigonometry make you masters similar triangle also. Today's session of similar triangles don't forget to join because I will teach BPD theorem and shortcut techniques I will teach you so that you can understand in the questions how and all you have to attempt the questions.

[00:17:04]Come on. By seeing this easy P by B that is tan. P by V is tan. Now some techniques are there. If you will write wrong means you will get a penalty. This is a game. Trigonometry is only game.

[00:17:17]Understood? And if you will write wrong mean penalty will come. Got it? Now which type of writing wrong answers penalties are coming? I'll explain you.

[00:17:26]Ratio is always coming in fractions. Now simplest form harsh ratio is always in simplest form means something was there common between the ratio part that we will eliminate and we are always writing correct now. So some rules I telling you this will Good morning Si. So this will be very important for you. Did you noted it? Did you noted it? Everyone ready?

[00:17:49]Online children are you ready?

[00:17:52]Monish mri all people are ready my voice is audible did you got this or not everyone sign opposite is >> coseant sign opposite is >> tan cos >> seeant is cos cos is secant now how they are coming opposite there must be something because of that they are coming opposite now the answer is yes they are inversely proportional so what is the relation is sin a = 1 by coseant a understood cos a is equal to 1 by secant a and tan a is equal to 1 by co a no doubt so this is a relation sin is is 1x cosecant a cos is 1x secant a tan is 1x Children make me strong by reading all the formulas again and again.

[00:18:54]Understood? If you people are knowing the formulas mean I'll be strong because you people will be able to kill the questions in no time. This is killing.

[00:19:03]Now we understand one thing. If tan did you remember one thing? Tan I wrote P by V. Why I wrote P by B? Because tan is connected with sin and cos we can write tan A is equal to sin A by cos A. That's it. tan a= sin a cos a and a mean reverse cos a by sin a no down after that we'll start killing them so now they'll not teach the bit they'll not teach you need to understand I'll be there now I'm there with you people so now tan a is equal to sin a by cos a and c a is equal to cos a by sin a please note down information is complete information if you know your yes so you need to learn you need to learn there's no limit of trigonometry nearly today I'm telling nearly 700 to 800 formulas I'm knowing if I'll start writing means I don't need book to remember the formulas that much formula I'm having inside me and trigonometry maximum formulas small small detailing of trigonometry I will do without using book that much is precious trigonometry is and how much command you have in formula now that much best you will be remember this how much command you are having in formula that much best you will be you need to remember this I hope are you ready for the next shot get ready now I'm giving you first question okay first question is done then Anything sitt this game now how much you are best in that that much you will been good in triometric. They have given three sides of a triangles.

[00:20:58]The sides are 5 4 3 understood. The three sides of a triangle are given 3 cm 5 cm 4 cm A B C. Okay. So this triangle A B C is right angle at B. Done. Now you need to find the value of first question.

[00:21:38]Six trigonometric ratios and second is sin a + cos b cos a + sin b.

[00:21:56]Six trigonometric ratios of angle A and angle C.

[00:22:10]No done everyone. Question please. P.

[00:22:13]Right. Pass this question. Everyone get ready. Please go on. Go on. Go on. Go on. Not down.

[00:22:24]Please. Write down. add the questions first.

[00:22:39]Ash, what is the social timing today?

[00:22:44]Social timing today.

[00:22:48]Huh?

[00:22:49]after can you tell ma'am today for 6 to 7 because seven I'll be taking maths today similar triangles I'm talking I'm not looking Are you all ready?

[00:23:26]Done. Shall we go for it?

[00:23:29]So, I'm going to teach this.

[00:23:32]Do you want me to attempt 100% I'll attempt? See, look here. First time I'm doing it, but I'll teach you one technique. See, correct. Super science. Sever also find out. Now, I'll teach you one thing. I told you now everybody please practice this one.

[00:23:57]Now one thing is there just arrange it.

[00:24:00]How you are going to arrange sine always should arrange with coseant tan always arrange with cord cos arrange with secant. This one arrangement work over done. Yes. Now when you are taking angle A, when you are taking angle A I'm this question I'm solving. Next question you are going to. So when you are taking angle A just draw here. See children always remember one extra drawing is not going to take you more. Okay. But it's a rough work for you. So this is angle A B C. Only one work you have to do. When a angle you are taking and b perpendicular you are taking this will become base perpendicular and hypotenus don't change symmetry understood not just b so here now this one will become four this one will become three and this one will become five for your understanding bp and h don't try to change the location this thing that thing no when angle a and together is there angle with 90° that will become base. Angle with 90° will become base. Angle with 90° will become base. I am repeating again and again.

[00:25:22]Angle with 90° though it's very late to join. Angle with 90° will become base.

[00:25:28]Now in shortcut technique we are going to do what was our shortcut way. This is the most easiest way we have got it. So now our base is four. perpendicular is three and hypotenus is five. And this was our rough work we did. Now base is what? Four. So where costs is there now you write here 4x 5. Remember this will become 3x 5. So now 3x 4 over. So this is 5 by 3. This is 4x3 and this is 5x4. Story over. How much fast I did?

[00:26:06]Done.

[00:26:07]What we did brain you need to this is a game. Trigonometry is a game. If you will play it soon nice you'll be able just try to grip it fast. What I did s one more time can we do it? Huh? Now what what is the angle s? A kava this was a and this was the b. When these two are taken together what it will become base. It will become base. So here this base what value is four and this is three and this is five but our B is four. Wherever B is there in cos B is up now. So just write B there and sine tan B is down. That's it. And after that full you will start perpendicular value will become three here.

[00:26:55][clears throat] Now we will go for the next one. Come on children you can do it. Please Rohit check this one out bit. sin C cos C sin tan C cos C coseant C see secant C that's it now here when C I am taking now in that triangle C was here and B is here and A is there now BC will become >> base >> BC will become base. So whatever the base is always three don't change the side here this is three four this will remain same but only one time you are going to take this as base and this time you're going to take this as base understood so alteration is there when you are taking both angles now here what is perpendicular four so 4 by 5 3x 5 4 by 3 by 4 5 by 3 and this one is 5 by 4 story was super that's what I was looking but here the values are different for these two people why previous 17 parts okay very good beta previous 17 parts were there we did it now please confidence is needed and don't get scared with trigonometry use scared trigonometric okay so now can we do it What was the values? Now we will we need some things to remember. Okay, because here something is needed until and unless that part is not there all see I cannot expect all the students to understand it one time but we will do it. Sham can you check one thing when I wrote A it came 3 by 5. When I wrote C, it came 4 by 5. That means beta hypotenus is still same. What is changing is perpendicular.

[00:29:07]S is perpendicular by hypotenus.

[00:29:10]Opposite by hypotenus. So sign only values are changing. For angle A it was three and angle C four. Are you understanding? So this only will change.

[00:29:24]Understood? Hypotenus remains the same.

[00:29:27]For cos also beta did you notice there?

[00:29:30]It was four and now here it is three but hypotenus remains the same. For tan it was 3x4 here it is 4 by 3.

[00:29:44]>> Angle is 90°. Why they'll ask angle B?

[00:29:48]They'll ask the respective angles which is with 90°. Understood? they'll ask the respective angle which is with 90°.

[00:30:00]Okay. So I hope you might have understood. Did you got this point or not? So if somebody will be asking you this question, are you able to answer the question please? Second part answer is 3x4. Absolute. So now look here.

[00:30:13]Second part question answer is 3x4. 3x4.

[00:30:16]Did you got 3x4?

[00:30:18]You got one. So let's check what and all answers are coming. Are you ready for it? Everyone have you understood?

[00:30:25]Everyone understood? Bes understood. So now I want one person to come and solve this. Rau, are you ready? Come solving. Yes. Second part.

[00:30:43]Go on. Go for it please. Everyone please check how he is solving. Now from here only we need to find the value. Sham please look here. Sin a we need after that cos c we need huh and then after that cos a we need and then sin c we need just these two values. So after the after we are making the values we just have to substitute the value. I hope everybody understood this one. Get ready please.

[00:31:13]Deepika are you there present online?

[00:31:15]Please answer the question.

[00:31:17]3x 5 and 3x 5 cos a is 4x 5 very good and after that sin c 4x 5.

[00:31:31]So it is coming as 3 + 3 >> 6 by 5 divided by 8 by 5 super. So 6 by 5 into 5 by very good cancel.

[00:31:49]So 3x4 is the correct answer. I hope everybody understood this.

[00:31:54]Yes.

[00:31:56]Very good. So 3x4 answer everybody got or not? Come on check. Huh?

[00:32:02]Shelam, you understood how to go for it?

[00:32:10]Online children, arashwini, yashika, I hope everybody understood.

[00:32:19]In trigonometry, you have to keep your brain very sharp. You have to keep answering the questions. Laksha, did you understood? Likita, did you understood how you have to? You got first one.

[00:32:29]Rohit understood. Super oil. Yes. So this is the way to answer the questions.

[00:32:33]I'm going to give you another question.

[00:32:35]Children get ready please.

[00:32:38]Yes we are going to go for another question. This is NCERTT question but I'll be giving you in a different format. Why to leave the simple questions?

[00:32:49]Uh I'll make it little difficult for you.

[00:32:54]Coseant A is equal to two given. They have given one of the six trigonometric ratios.

[00:33:03]Coseant A is equal to two given.

[00:33:06]Trigonometry this year was horror story in board exam. We will do it very clear carefully and dedication is needed.

[00:33:14]Okay. If you're not understanding immediately ask I did not understood because it's about your career.

[00:33:20]Coseantly given as 2.

[00:33:24]Find 1 by tan a plus sin a by 1 + cos a and your time starts now.

[00:33:42]Uh denominator in the beginning we need to check up and down cancellation is not there.

[00:33:57]Come on, come on, come on, come on, come on. Go for it, please.

[00:34:03]Exam time better. We must be doing that.

[00:34:09]Come on. Come on. So, can I draw it first? So, we we are going to perceive certain things. Please understand this one. First, I'm going to draw a triangle.

[00:34:20]So when we draw the triangle angle a we will keep near the triangle. So this one will become a b and c. One work done.

[00:34:30]Then coseant a. So here one thing is there. Please check this one out. This is a given and this is 90.

[00:34:40]So this one will become what beta and this one will become perpendicular and this will as usual will remain hypotenus. Now our story is we know cosecant coseant a is what better hypotenus by >> hypotenus by perpendicular because sine opposite is there. So hypotenus by perpendicular. So here what is given two perpendicular not given anything means one understood. So if coseant is 2 by one huh hypotenus is two because they have given the value two they did not give because see here nothing written means 2 by one nothing written means 2 by 1. If they'll write like this. Now please understand this one. This is five and here it is written as three. Then how we are going to write? Coseant is equal to 5 by 3. But here nothing written. If they will write coseant is equal to coseant a= 4. That means what we are going to perceive 4 by 1. Now is it clear children? Come on say is it clear hash? So this part only we are writing 2x one but you're not supposed to write 2 by one. It is in ratio format children again and again I'm speaking something listen it is in ratio and ratio is always in the simplest form. So we can't take like that. What is the rule here is when you are writing two by one you have to multiply both with x. Please please please understood because what was common you cancelled when you are writing 10 by 20 what you are writing after cancelelling you are writing one by two what was common you have killed 10 correct now so that means the common part always we are eliminating. So at the time of ratio writing and converting the ratio to get some values we have to write that common part which we have removed. So x can be any values. x can be any values. So only we are implementing what x don't write x and y. Always write same value because that only got cancelled. Now here 10 by 20 sham. So 10 only was common. Correct?

[00:37:04]So that was 10 was up also 10 was down also. So here if I'm writing up x up means x also down we have to write. Now bit coseant is what? Hypotenus by hypotenus by perpendicular. So hypotenus became 2x perpendicular became x. So now use pythagoras theorem. So now here we are writing here we are going to start in triangle A B C right angle at B what we are using using Pythagoras theorem what we are using here is Pythagoras theorem and you know in Pythagoras theorem what you are doing children in Pythagoras theorem hypotenus the longest side AC a c² will be equal to bc² + a square hypotenus square is equal to perpendicular square plus ba square don't do publicity stand by writing this that mistake coming means nobody will be there to save you that time Understood?

[00:38:25]Don't directly write. Just write the rule first. Hypotenus square is equal to perpendicular square plus base square.

[00:38:31]After that substitution now shift here and there that is not at all a problem.

[00:38:35]Here base was missing. Now many student they do what? They write base square is equal to perpendicular square minus hypotenus square. They only killed. So publicity stunt is not needed. What is the formula? Hypotenus square is equal to perpendicular square plus base square. Mistake will not be there. I hope you people have understood. So now come on go for it. AC will become root under what is your BC?

[00:39:02]X² and there is no tax for putting bracket.

[00:39:07]Many student they do like this x² + 2 x² mothers here big mistake is this one because here square is only on x not on two. So when two number are going are going going for a squiring here you have to do like this give respect understood this is earth and this is an earth understood after that nobody will save you after that you will only cry I wrote everything why they are not giving me marks you're not following the rules of mathematics understood or not so where vowels are needed you cannot put consonant so what is needed in mathematics mathematics is the subject is a language language of science and symbol rules are there. They made it this rule and they kept teaching you in junior classes. You kept ignoring those things. Now it is going to give penalty in higher classes why children are not getting full marks. The reason is you are not listening the rules. That's what is the problem. Understood? So here what answer will come? Come on. Say Amish. AC will become what? X² + 4 X². What it is coming boss?

[00:40:18]>> X².

[00:40:25]>> Yes.

[00:40:28]>> Okay. Okay. Very good. Thank you. So this is coming as 2X². BC is coming as X². And this part is AB. We have to find AB square. Thank you so much. So now here a b square is equal to now can we do it? I was discussing and I did mistake. See so b what we are going to write 4x² minus x² it will shift that side. So here it will become 4 x² - x². Now can we take root on both side? Once we are taking root on both sides how much it will become 3x². So what is a roo<unk>3x x? You take it out. Have everybody understood? So root this one will become roo<unk>3x. That's it.

[00:41:14]Now you are ready to solve.

[00:41:17]>> No no no no only plus root three sides.

[00:41:21]Here you are supposed to take plus minus but we will take plus here for trigonometry for some part because it is a distance and distance is always measured in positive. There are certain rules we need to follow there. Got it? H roo<unk>3x base is coming as roo<unk>3x.

[00:41:42]Now let's see we are able to solve this part or not. Get ready everybody listen me carefully. This is the most important sections please. So now look here once you did till here. AB is equal to what is AB? Now you have all the values base perpendicular is X and this first one.

[00:42:00]What kind of things are here? tan sin and cos with much sin a is x by 2x cos a is <unk>3x by 2x tan a is x by <unk>3x this this this this this cancel understood all the three whatever values were there we cancel x now whatever we have taken Because again we reach to ratio and in ratio when you are writing x will get cancel common part will get cancelled. We utilized it what we utilized we utilized x only for using hyper what you call pythagoras theorem because that time we were considering sides. Okay that time we and mathematics says that the sides when ratio you are finding kill the common part but when you are using sides take the proper value. This is the pure part of mathematics. We must not leave. Now are we ready for solving the question?

[00:43:05]Because everything we have done till here. Now question is 1 by tan a plus sin a by 1 + cos a. Can I say you something? What did I taught? 1 by tan a is 40 a. 1 by tan a is a. So here it will not tax a lot. Cot what is your sign value 1 by 2 plus what is your s cos <unk>3 by 2 and beta c a is what?

[00:43:48]Base by perpendicular. C a is base by perpendicular. What is your base? Beta c a base base. It will become <unk>3 by 1 + 1 by 2. Take LCM 2 + <unk>3 by 2. Easy.

[00:44:09][snorts] <unk>3 1 by 10 a will become cot. So directly roo<unk>3 <unk>3 + 1 by 2 by 2 + <unk>3 by 2 that means it will come 2 will go up 2 + <unk>3 will go down. So this and this will get cancelled. So here it is coming<unk>3 + 1 by 2 + <unk>3 multiply roo<unk>3 2 + <unk>3 + 1 by 2 + <unk>3 people they tell that don't keep root on both down so 2 - <unk>3 and 2 minus roo<unk>3 one shot we are rationalizing also please remember children rationalization is very important don't Leave rationalization little bit trick will be there. See many many many many times in notebooks I have checked you people are writing first part absolute correct you people are writing till you know what I saw one thing here only you people are killing full part of mathematics not only killing you are putting them in hell calculation solving section is problem who is the most smart person who will come out with this problem correct so now look here one thing I did please first this will become 2<unk>3 + 3 + 1 and then here 2 -<unk>3 a + b a - b a² - b² now here it will become 3 + 1 >> 4 4 so 2<unk>3 3 + 4 and here 2 - <unk>3 denominator part will become 4 - 3 4 - 3 is 1. So this 4 - 3 will become 1. So now we are going to multiply 2 2 4 <unk>3 2 4 8 roo<unk>3 <unk>3 - 2 3's are 6 and then this into four means - 43 and denominator part is one this and this cancel that's it that's what so only I told you now penalty sections if you will be writing till here maximum how much you will lose half marks you are going to get from here minus They will not have mercy on you also.

[00:47:10]They'll not have mercy on you. The paper correction techniques they are not having mercy on you. They'll not take you as human. They'll take you as machine. Your brain should work to finish it. So whenever whenever children denominator is having irrational number, rationalize it. Understood? Rationalize the rules of mathematics. If we forgot means they're giving us penalty. Those many people are fewer sports. Now in sports what they doing? If you're doing mistake mean they giving penalty or not.

[00:47:37]Same here mathematics also it's a sport.

[00:47:40]When you will do mistake you will get penalty and they'll cut marks. Many students they do like this. I have seen 4 + <unk>3 by 8. They do like this.

[00:47:55]>> Many children are doing like this. Four up four down by how they you can cancel this and this? You have to first take out common in numerator and then you can cancel. Are you understanding? Because I have seen many people. Yeah. From 20 years I'm seeing this type of mistakes only. Are you understanding or not? So we have to be very careful. Are you ready for the next question? Come on get ready. This time you people are going to solve. Huh?

[00:48:27]>> I kill you. For that only I told take x.

[00:48:33]They will answer will come anyways but procedure is wrong.

[00:48:39]Sir you are writing board good examination first you must understand it's in addition. Yes. So the thing here is please it's in addition. Very nice.

[00:48:50]Thank you so much. That is addition rule and that's the most important part. If I will see this in your note next time I seriously go your hair here I will give to kundal for either balaji or muran no we are ready for the next question please get ready for the next question children good morning >> are you ready for the next question two steps.

[00:49:33]>> Okay, I'm writing here question.

[00:49:47]Are you ready for it? Your question is right angled at C.

[00:50:08]If tann is = 1 by <unk>3 find the six trigonometric ratios for angle C and your time starts now.

[00:50:41]I'm not going anywhere. Please, how I will leave you people and go. Please.

[00:50:47]This is the next question. Go for it.

[00:50:48]I'm solving.

[00:50:51]This is a competition question. Come on, go for it. Tricky. Not tricky at all.

[00:51:05]As the exams are near now morning 5:30 itself you wear the uniform how K students are doing and get ready and join the sessions in this way now few months of hard work and training will train you and change you a lot understood sorry 42 First this multiplied with this 4<unk>3 then this multiplied with this 8 already you wrote then this multiplied with this 2 into <unk>3 <unk>3 it will become - 6 look better this multiplied with this 2<unk>3 into roo<unk>3 roo<unk>3 <unk>3 will become 3 into 2 6 and then this one will multiply it means - 4. Very good you asked. Please ask me, sir. And please check everybody. Please check.

[00:52:08]>> Huh?

[00:52:09]Uh, six trigonometric ratios you have to find. Now look, can I start my work please?

[00:52:14]>> They told C. Why I'm going to ask for angle A?

[00:52:22]>> Oh, right angle. Let's see. Right for B.

[00:52:29]Come on. Come on. Come on. B right angle at B for angle B.

[00:52:37]I wrote right angle C now. So that time I write mean I write angle at B.

[00:52:45]No problem.

[00:52:47]Hey sides right properly.

[00:52:51]Can I do this please?

[00:53:02]Super you're going very good go finish it finish it amish nice only presentation hash you're doing too much of cutting splitter three things you always write whenever you are drawing first thing is drawing for trigonometry first you draw the triangle without drawing don't do they told right angle at This part will become B. B I kept near.

[00:53:34]Okay. When you are taking tan A, tan A is perpendicular by base.

[00:53:40]Correct. Now for tan A, perpendicular by base. For A angle, which one is perpendicular?

[00:53:47]Up or down?

[00:53:51]For angle A, which one is perpendicular?

[00:53:54]Down because this one will become base for angle A. Now, this one will become base. Angle A and C is together. So, this one will become base and this one will become perpendicular. So you first write<unk> 3x and it will become x using what theorem boss using pythagoras theorem what theorem pythoras theorem pythagoras theorem says that hypotenus² is equal perpendicular square plus base square.

[00:54:38]We don't know what is AB just one.

[00:54:51]So what you are getting a = 4x² root is coming as 2x. So now a is coming as 2x.

[00:55:05]Now our six trigonometric ratios. Now B is the angle and C is 90°. So this one will becomes base perpendicular and hypotenus. See for tan A. Now why they what they did is tan A they give and there they will get confused. You'll write here root3 and here you'll write X. Here only the entire story will become over. Has she done? Come on here submit.

[00:55:33]Wrong or right we'll see afterwards Jerome what happened hypotenus is to absolutely correct first who I have given root four is to absolute correct box but don't forget x please again and again I'm telling don't forget x and write it properly so many children they have submitted you people can type and send just just send sin a cos a and tan a value so now here sin b opposite is coseant b cos B opposite is secant B tan B opposite is >> C B sine is now X by <unk>3X here it will become <unk>3X by X I'll write with different color so that they can understand this it will become<unk> 3X by 2X sorry perpendicular now X by x by 2x and here it will become 2x by x. cos is <unk>3x 2x and it will become 2x by <unk>3x. tan is x by <unk>3x and here it will become <unk>3x by xx. After that x you can kill answer is coming here.

[00:57:01]Uh angle at C it was magnet. Angle at C means 90°. Everything will become Goinda Goinda.

[00:57:18]First is G.

[00:58:24]Next is Oh this is my so today evening everyone today evening again you have this session similar triangle see this is the month of hard work after that from September we have more hard work October November November means you will not have time to smile also That much torture I will give to you till you will not get perfection. We will not be stopping. Understood? First thing is better for whom I'm doing this for me or yourself. But once you will get the score, you'll not remember me also. But only one thing will be there.

[00:59:18]Huh?

[00:59:19]>> No. Why I'm telling you? Because most of the student they do like that only.

[00:59:22]Nearly how many students I trained? I don't know. But the most important thing is please study for yourself. Not for your parents, not for your teachers, for anyone. Get the best because you people are having that caliber. So please utilize that caliber at today evening.

[00:59:38]What time? 7:00 social ma'am. Huh? 7:15.

[00:59:43]Okay. So inform social ma'am you finish 1 hour before just request.

[00:59:51]>> She's keeping 6:00 only. So 6 why?

[00:59:53]Because I want this session you people to understand similar triangles parallelly. I will run both the chapters together and coordinate. I think in Sunday one day I will take seven to eight hours coordinate geometry because sample paper exams are coming I have to give revision also.

[01:00:09]Yeah. For whom I'm doing this?