day 9

[00:00:04]Let us see, in the previous class we had studied about completely complementary angles which are called complementary angles. Babu, in complementary angles you had studied till question number 25, by doing sin 90° - theta, today we are moving ahead from question number 26, let us see 25 from question number 26.

[00:00:58]26 Babu is telling you that cos was not given here, cos is also given in the form of cos, this is also given in the form of theta, in the form of theta, Babu, let's change this also in the form of theta and this also in the form of theta, if we change any one cos or sin, then we can write cos Babu, cos we can call this sin 90° minus how much sir theta + theta and how much of this minus will it become sin 30 - theta, this will not become the sine of sin, if we take this 90 minus into 90 then minus now how much theta is there of minus, Riya, sin of minus will become 90° - theta. How much will this sin be subtracted from this? 30 - sin of theta minus and this 30° minus how much? Theta. Are both the same? If both plus and minus are cut then what is the value sir? 0 One of them has to be changed. If you feel like changing the sin, you can do it.

[00:02:22]Like if cos is 60° plus what is it, Babu? Theta. Now what is the sin of minus, sir?

[00:02:28]30° minus theta. If you feel like changing it, you can do that too.

[00:02:33]So what would you write this as 60 plus theta minus? cos 90 will not be written like this.

[00:02:39]What will you write, Babu? This is what cos 90 minus 30 - theta will write. So this becomes cos and this is 60 plus theta minus cos of theta, how much is this? 90 - 30 plus how much? Theta will not be made here, Babu. So this cos becomes 60 plus theta and what is the cos of minus, 60 plus theta will be cancelled by both of these, so the value is zero, if you change any of the two then what will be the answer sir, it will remain the same whether you change cos or sin, similarly let's see the next question as it was given in this, Babu, you have to change, so I told you this type of question, we will change any one, whether up or down, you said up, up, can we write this, how much is sin 90° minus 55 and also how much is cos 55 below, write it correctly Babu, write it correctly, then cos will come, sir, write it correctly and how much is this of plus, change any one, up or down, up, so we will also get cos 90° minus, now brother, how much is this below also, how much is 2 * cos of minus, Babu, this will become 60, this will become 16, let's subtract this from this, so how much is cos cos 55 and How much will cos 55 become below, the whole square will be formed, how much will cos 35 become, how much will sin 35 become below, the value of minus 2 * cos 60 will be 1/2, will it not remain the same, will these two be subtracted from these two, when these two are subtracted from these two, then the value will be one, here also the value will be one, if we square one, then one plus will become one only, Babu, and how much will minus be subtracted from two, will this also be the value one, so this 2 - 1 will be one, in any condition the value will come from whatever value is there, the smallest value will come, sir, next after 27 we will see 28.

[00:05:00]Babu, one of them has to be changed in this also. I will change one of them. Ok? Whom should I do sir? Which one should I do 80 or 10? Whom should I do it to? We will do it on 10th, sir. We will change 10. It is necessary that we do it on 80th. So we can write this as sin 90° - how much?

[00:05:20]And don't say 80. Change one of them.

[00:05:23]Whom should I do it to?

[00:05:26]cos or sec cosec to cosec to cosec.

[00:05:30]So what is the cos of plus?

[00:05:34]Babu, you can write 59 and into, this will be cosec 90° minus 59, it will become 31 n.

[00:05:43]How much of this cos do I have? What is 80 minus? cos 90° - theta is how much? cos yes plus how much did it become? What is cos 59 cosc 90° - θ? sec 59 this did not happen. If this is cut then what is the value? One and cos * sec also has the value one.

[00:06:03]So how much will we get if we do 1 + 1? Two. Correct? We will see it carefully. One more left. There will be two more questions in this. This type will also be completely completed. Now from here sir let us look at the identities a little. Yes.

[00:06:20]Now from here the entire question will be based on identities only.

[00:06:22]Then look at it a little carefully.

[00:06:25]Perhaps we had taught you Babu that we should look at sin theta very carefully.

[00:06:32]1 / How much? You can say cosec.

[00:06:36]Then what did you write after that, Babu? cos theta to what one by how much? sec. Then after that Babu, how much is tan theta by one?

[00:06:47]Then we wrote that maybe what will we write for cosec theta also?

[00:06:55]Then what did we write after that Babu, what can we write for sec theta also?

[00:07:01]Then what did we write after that, what will we write for cot theta?

[00:07:07]Then it was also written that maybe we can write tan theta as sin / cos and what will we write for cos Babu? What will you write for cot?

[00:07:20]How cozy? Sin After this, these six cows were also probably written.

[00:07:27]Then Sir, you must have also told these six Go that after this what is the value of sin theta * cosec theta? It will become a forest. Then what is cosθ*, Babu?

[00:07:44]How much is this cost*? sec theta also has the value one. Then this was also written Babu.

[00:07:52]tan theta * how much is it? What is the value of cot theta? Forest. Isn't that it?

[00:07:59]After this, I also wrote this to you, Babu.

[00:08:02]No, we will stop now and say sin 90° - theta of sir.

[00:08:10]Costa had created questions in this just recently.

[00:08:14]What is theta of cos 90°? sin theta. Then what did you write? cosec 90° minus theta of what?

[00:08:25]sec theta. Then what did you write Babu?

[00:08:29]sec 90° minus theta of what?

[00:08:34]cosec theta. Then how much after that?

[00:08:37]What is tan 90° - theta, sir?

[00:08:42]Babu, how much did you study after this cot theta? cot 90° minus how much? Theta so how much is this?

[00:08:49]tan theta. Correct? We have come this far after studying.

[00:08:52]Then after this Babu.

[00:08:58]Yes.

[00:09:05]Okay, we will see, Babu, had you told me sometime that the value of sin² theta plus cos² theta is one, right? So, we will only find the value of sin. If sin² theta is 1 - cos² theta, if the square is removed, then what will happen Babu?

[00:09:28]1 - how much. Then after that, if we take cos, then cos² theta will be equal to 1 - how much.

[00:09:40]If this sin square is removed, then what will happen Babu? So, how much will cos theta become? 1 - then we had studied, Babu, how much did we study, how much did sec² theta minus sec² theta have, the value of tan² theta is one. Did you get it written like this? What is the value of sec² theta - tan² theta? Forest. This is what will happen.

[00:10:07]If this minus goes there, how much does it become? Plus so sec² theta is equal to 1 plus what? What will happen if the square is removed, Babu? What if Square goes away? Root.

[00:10:20]How much is this under the root? 1 plus how much?

[00:10:24]Correct. Then after that Babu, if you see, we will take out the tan, brother. We did not take out this even for sec. If tan is in minus then what is tan² theta equal to minus?

[00:10:35]1 - sec² of theta. Correct?

[00:10:39]If we subtract the common from both of these, then what will happen if we subtract the common, sir? So tan² theta if we take common like minus then sec² will come forward and where will one go?

[00:10:50]Back. So these two will be cut from both of them. So we can write tan² theta equals what?

[00:10:59]What will be the formula of sec² theta - 1 and only tanta sir? Root sec² theta - of 1 last ago blue will not appear. You will see blue in this, see blue, what will you write after that sir?

[00:11:20]What is the value of cosec² theta minus cot² theta? Forest. Is it visible in this too or not sir? Can you see it or not?

[00:11:31]not visible.

[00:11:39]One step we have to do is reduce zooming. We will do the same in the end. We will open slide one. Is the board main or small sir? Did it come in full?

[00:12:13]Ok.

[00:12:15]You will see.

[00:12:17]Remove the color. Isn't that it? What did you just say, Babu, what is cosec square of minus theta?

[00:12:27]What will be the value of cot squared theta? Forest.

[00:12:31]Ok?

[00:12:32]So Babu, we can also write this that if we go cosec² theta or minus then what will happen? Plus 1 plus how much will it be?

[00:12:41]cot So if we just find the value of cosec theta, how much is left under the root? What is 1 plus? cot² theta Then if we calculate cot in the same way, how much will it become minus? What is cot squared theta equal to? 1 minus how much? cosec² theta will become this. If we can take minus common from both? As soon as we take the minus common, cosec square theta will come forward and how much of minus? 1 Will both of these be cut? So this is cot squared theta equal to what? So this cosec squared of theta minus how much?

[00:13:17]What will happen if 1 square is removed, Babu? So how much is the root under, Babu? cosec squared of theta minus how much? 1 Now the identities will be complete in this much, sir. Now you have to keep this much in mind. Okay, right? Yes, sir, we had come here after studying this thing. Babu, what is the value of just sin² theta or sin² theta plus cos² theta? Forest. If we had let it stay here, what would have happened if this plus had gone there? You just have to understand nothing. What is sin² theta equal to? 1 minus how much is it? cos² theta cannot sit upright.

[00:13:54]What will happen if Square moves? So root under 1 minus what is it? cos² will become theta. In the same way let sister cos² stay.

[00:14:02]If this plus goes there, how much does it become?

[00:14:04]Minus 1 - sin² theta is done, sir.

[00:14:08]What will happen if Square is removed? Root. Did the same thing. And sec² theta - tan² theta equals what? Forest. If sec² were allowed to stay. So what if this minus goes there? Plus, if this plus does not become plus and the square is removed, what will happen? Root. Similarly, if we find sec now, then we will find tan also.

[00:14:26]So tan was in minus and this plus went there, what happened? Minus. So what do we take in common from both of them to remove this minus sign, sir? Minus. Like if we take common minus then both the minuses will be deducted.

[00:14:37]So tan² theta is equal to what? sec² theta minus if square is removed then what will go again sir? Root. That's what happened. Then in the end also sister did the same thing that cosec square theta minus cot square theta is equal to what? Forest. If this is cosec squared theta. So what if this minus goes there? What will happen if Plus Square is removed, sir? Root. Now whose thing did you take out?

[00:14:58]cosec ka na. Now what is the remaining part? If you take cot cot then it will come in minus.

[00:15:02]And what if this plus goes there? Minus. When minus common was taken from both of them, then minus was subtracted from minus from both. This cot² theta is equal to cosec² theta minus how much?

[00:15:12]One will be cut from this and the square will be removed, then what is needed, see if this thing is not left and the square is removed then what happened, come on root, tomorrow everyone will write this thing in one page sir, okay, don't you understand, if you have the formula in front of you then only it will be completed otherwise it will not be completed sir from here, yes, write this entire thing in one page, take that chart paper of ₹1 sir, write it completely in it, sit with it and then the question will be prepared from here otherwise not even a single question will be prepared, it is better if you memorize it. If you don't remember, at least you should see where you drove it? I will always do this tomorrow, sir. Yes. Yes, now the entire total will be given to you directly.

[00:15:53]So directly we will use sin theta.

[00:15:54]So you will keep asking us again and again where did you get it from. Then that thing will be known. When you make something and you see it, you will remember it quickly, sir. Okay, right?

[00:16:03]How and where will it be used. For example, the question right now is sec² 9 sec² theta sin 9 sec² a, how much is the minus here? If it is 9 10 then what will be its value sir? Ok?

[00:16:15]Let's move on to the next question. Okay, as you have this question Babu, was this what was given? Your identity completely starts from here sir. Understood?

[00:16:26]Now from here the question will become more. Let's take the question out, sir.

[00:16:45]This is the question I have. So let's take this question. Babu, I had asked the same question like you, what did you have for 9 sec² theta and minus? If we talk, do both of them have nine, sir? What will happen if we do not take common? sec squared a minus how much? tan² and the formula for this thing is written that what is the value of sec² theta - tan² theta? If we do 9 * 1 then how much will it be sir? 9 is done. Correct. I do n't want to see this anymore, sir. Now you should write it down tomorrow on chart paper, only then it will work sir.

[00:17:29]Ok? As we move on to the next question, Babu. Let us show you that the answer will be the same in all cases.

[00:17:34]This is it Babu.

[00:17:36]This question was given to you.

[00:17:39]If this becomes LHS then what is it to me? RHS. So if we talk about LHS, what was the value of LHS given by Babu? I have sin to the power 4theta and cos to the power 4. Can we write this thing? Whole square of sin² theta too and what will you write for it, Babu?

[00:18:00]How much whole square of cos² theta is the formula of a² - b² will converge once, it will converge once and what happens once? Will decrease. So sin² minus theta becomes what? cos² becomes theta.

[00:18:12]In which did you break it, Babu?

[00:18:16]What is the formula for a² - b²? How much of a + b * a- b a -? This is what will happen, b a - b.

[00:18:23]You read that the value of sin² theta + cos² theta is one inu how much is left?

[00:18:29]What's the sine squared of minus theta?

[00:18:31]cos² theta If we multiply something by one, how much will it become? One, so what is this sin² minus theta? cos square theta. This is what had to be proved. So we will write LHS equal to what should sir?

[00:18:43]Correct. It was four. We broke both of them on the square for four. What is the sum of a² - b² and a + b - a? b How much does it swell? What is the value of 1 sin² theta + cos² theta? Forest. He remained as he was. Got everyone introduced to one person. Ok? Then we will see the next one, Babu.

[00:19:02]Like you had it given to you. This is the question.

[00:19:05]This is it, isn't it, Babu, how much do we have to bring sin theta * sec theta and then tan theta * tan to equal? tan. Can't we see this sin sinθ, Babu? Can we write to sec? 1/cosπ is correct.

[00:19:19]What will happen if we get an intubation done from one person?

[00:19:22]Whose formula was sinta/costa? So it will not become tanta's.

[00:19:25]Like how much value of cos * tan do we have to prove? sin then cosθ can we write tan? sin / cos sin / how much? cos what will be cut babu?

[00:19:36]What will be left after cos of cos, sir?

[00:19:38]Correct. Isn't it right? We will see further later.

[00:19:44]Now it will be ready slowly, sir. Why are you taking tension? will form.

[00:19:49]We will see a little bit. This was the question given to you that sinta + cos 1 + sinta and 1 - how much cos, so if we take the LHS then how much is sin theta of 1 plus and how much is sin theta of into 1 minus, if a + b and a - b then a² - b² is the square of one, then what will we write into Babu - we can write sin², we can write it, we will square one, so what is one? It's like sin² theta of sin² theta. I just told you what is the value of sin² theta plus cos square theta? Forest. Isn't that it? If we are here, who is at fault?

[00:20:33]What can we write if cos² theta equals?

[00:20:36]What do you write where 1 - sin = 1 - sin² theta? cos² becomes cos² theta. Then after this Babu had written that we can also call cos theta as 1/sec sir.

[00:20:49]Can you write? So if we write this as 1 / sec then what will we write? One by how much?

[00:20:55]sec square theta. This is what you had to prove, sir. Like here also we will see cosec square theta sorry cos square theta in brackets one plus what is it?

[00:21:07]What is the value of tan² theta minus tan² theta, which was just written behind? Forest.

[00:21:09]What happens if sec² theta goes to minus there? 1 plus how much? What can I write for tan² theta where it is 1 + tan² theta, sir?

[00:21:18]How much did you say into sec?

[00:21:21]sec² theta is squared to both bases, so we can write this as cos theta into what? We can call it the whole square of sec theta because if we square it then we will square it as well, so just before we wrote what is the value of cos theta * sec theta, sir? There is no forest.

[00:21:37]So what will happen if we square one? Forest is correct.

[00:21:43]Yes, we can write it in this, what did you say, it means both LHS and RHS are identities, sir, we have to use identities, sir, whatever there is, we have to use all the identities, can you please solve it today, sir, we will see Babu, after this, you were given this thing, cos² theta, Babu, so we should write cos² of cos², 1 + tan², still behind it is 1 + cot², right, just now it was said that the value of cosec square theta minus cot square theta is one, so can we write this as cosec square theta equal to what, Babu, it will become 1 plus cot square theta, right? So what would you write in its place? cosec² theta is correct. Then after that I just made you write that cosec theta is one by what? If you look at one, what can we write for sin theta, Babu? You can say 1 / cos cosec cosec theta, sir. So this is also 1 / cosec, right? So what will we write about this?

[00:23:03]What is cos² plus theta? So what is the value of sin² theta + cos² theta? 1 This is what I had to prove. If you look here also, 1 + tan² is like this 1 + tan² a + b and a - b, so what is it? What happened to a² minus?

[00:23:19]This is what will happen. Should I square it? Okay, how much is 1 plus this? tan² is done. If we square one, will we square one of this? Correct?

[00:23:31]What can I write in its place? sec² and how much in its place? What is the value of cos² cos * sec? Forest. Square one of 1. Correct. If you remember the formula, it will be done quickly, if you don't remember it, it will never be done.

[00:23:43]Okay, right? And you should remember that you will find all these types of questions filled in, sir, no matter how much you remember, there is no solution. Please copy it, it is mischief, sir. The person sitting on the back bench's mobile is working, so is it working sir? Yes, hey, a live man is standing here, look here sir. Yes, a live man is standing here, look sir, you will see it when it is new, live sir, it is made for the future, let's see Babu, what is this costa + sinta square and costa minus? sin² theta So we can think of a as a whole. How much to complete this? b this also a and this also how much? b if the formula for the square of a + b is a² + b² plus how much? 2ab means how much will it be Babu? cos² b² means how much?

[00:24:57]Plus 2 * how much?

[00:25:00]How accurate is this? Then the formula for a² - b² is a² + b² minus 2 * cosθ * how much? This is what sin theta will become. If you look a little carefully, if you had a cos 2 coshet * sinta here and a cos this was in minus, would the plus and minus be subtracted? The value of this whole is one, the value of this whole is one and one, how much sir? Correct. Moved forward and did nothing. a + b² and a - b² then how much of a² + b² plus? 2ab a - b² So how much of a² + b² minus? 2a these two plus and minus cut. sin² theta + cos² theta has the value one. What is the value of sin² theta + cos² theta when one plus one is added? Two.

[00:25:55]Correct.

[00:26:00]Babu, this is not what I gave you next.

[00:26:04]If only this thing had been given to me. This will become LHS for me. What is that thing? RHS. Please take a look at it carefully.

[00:26:10]When we take the LHS, you probably have cos to the power 4a - sin to the power what? 4a This is what I gave. Can we write this thing down? The whole square of cos square a is also and what will we write this Babu, how much is the whole square of sine square a, so the formula of a² - b² will be added once, what will be the subtraction once, so how much will the sine square of cos square a plus become, what will the sine square become once Babu, how much will cos² a minus become, this will not be the same, let's say the value of cos² theta + sin² theta is one, that remains incomplete, so how much will this cos square of a minus become? And if you multiply anything by one, it will remain the same. So this becomes cos squared a - sin² a. Now, in which proof should we bring it, Babu? cos in cos in na. So we just read what is the value of sin square theta plus cos square theta?

[00:27:10]Forest. So whose value should we find out from this, sir? Find the sine of the square.

[00:27:18]Babu, what will happen if we find the value of sin² theta? 1 - cos² theta is what will be formed. So wherever there is sin² theta, we can write 1 - cos² theta, sir. So what is this cos square?

[00:27:31]What's the cos square of a &minus a &minus 1 minus?

[00:27:35]Write cos square a correctly.

[00:27:38]What will happen if you get it into minus, sir? Cos squared becomes 1 of minus cos² of a plus cos² of a.

[00:27:43]It's a go and a go of go.

[00:27:48]How much is 2 cos²? You can write a - 1, sir. Correct? So what do you write on the LHS equal to? What did the RHS do? What is the square of four, what is the square of this, what is the square of this, a² - b² formula a + b a - b, what is its value? The forest remained as it was.

[00:28:07]What is cos² a minus? Sine square a was to be proved in what? in cos na. So who will have to change sin to make cos. So let's read what is the value of cos² theta + sin² theta? Forest. What if this plus goes there? Minus. In whose place was it written, Babu? What should be written in place of sin² sin? What will happen if 1 minus minus is added into one and one plus one is added? Two. Whose sign is in the middle? Minus. Correct? This is the next one, is n't it Babu? You have to prove this thing, what is sin theta plus? cos theta. When we take the LHS, what is the LHS? sin na babu how much is this sin ta and plus? cos perhaps we had read the formula a - b.

[00:28:57]Sir, does anyone remember the formula of a + b Sir, what is a + b and into, Babu, what is a² minus ab plus b², maybe this is not the case, so if we talk about it, what will be formed in a, Babu, so what will be formed in a will be sin and what will be formed in b will be cos, so first of all what has been said about a + b, then what will be written in place of a + b, sin theta plus how much cos theta will be written. Then what did you say Babu? What did he say next? What is a² in place of a²?

[00:29:32]sin² theta minus ab so sin theta into how much? will become cos theta.

[00:29:43]How much did it cost in place of b²? cos² here, can we say cos² theta? Correct? Babu, it remained the same as it was.

[00:29:52]What is sin theta plus? cos theta.

[00:29:55]Now come on, in place of sin² theta + cos² theta, how much is 1 minus, how much is sinta * how much cos, how much was to be brought sir, how much was to be brought, the same thing was to be brought sir, so we did not do anything, how much is the sin theta and plus cos theta, what should we write about this, Babu, how much is a taken from 1, then what will be the formula of a + b, a² -ab plus in a + b, so the formula of a + b is the same, a + b, what is a² minus a²? Let us consider ab + b² as a.

[00:30:32]What does one mean? b a + b a² minus how much? How much of ab and plus?

[00:30:39]What is the value of 20 sin² theta + cos² theta? Forest. The rest remained as it was. Ok? Move ahead.

[00:30:48]Let's see further.

[00:30:52]This is not all I gave, Babu. Please take a good look at it.

[00:31:02]Listen carefully. This is what I gave you Babu. Should we do this? 1 plus if we look here, what happened here is that we have cosec² theta minus cot square theta? Forest. This is cosec square theta, Babu. How much can you write of this 1 plus?

[00:31:34]cot square theta right? Well, we have a cot upstairs, right Babu? What will you do to make a cot? So this cosec² becomes theta and plus comes here minus. How much did this minus go there?

[00:31:46]Plus. Can you write it? cot² can be written in the place of theta.

[00:31:52]What are you writing, Babu? So if we add cosec², how much is theta and minus 1 by the bottom? What can we say is 1 + cosec theta?

[00:32:02]Correct? If we call it the square of one, then is there any problem? Because what will be the square of one? One. And we also read earlier that what is the formula of a² - b²? a + b * how much? a - b is what happens.

[00:32:16]So what does one mean by a² ako? 20 So this 1 plus can we write it once? What is cosec theta plus 1 and into, Babu? What is cosec theta minus 1 by down? 1 + cosec theta is going to be this. Did you find out whether the one with plus one will be cut from the one with plus one? What will be left? 1 plus this cosec of theta minus 1, right. Did the plus and minus get cut? What will be left, sir? You can write cosec theta, sir. Didn't do anything.

[00:32:47]What should I write where cot² theta was? cosec² theta minus how much? 1 So cosec² theta - 1 one we can call 1 squared, right? So will the same thing be cut from both a + b and a - b of a² - b²? This forest became a forest. It just happened the way it was. If the minus and plus are cut off, what will be left, sir? cosec theta. Correct? Then the next one is in the same manner. This is sec to the power 4 and sec² theta. Sir, is it right?

[00:33:16]If we talk Babu, then if he has four, then can he take two common ones with the two people next to him? If we take two as common then what will be left with it sec² theta, Babu?

[00:33:29]sec² theta and minus 1 is what's left.

[00:33:32]We just read what is the value of sec² theta minus tan² theta? 1 is correct?

[00:33:40]This is tan square here, if you look at it, Babu, one step what can we deduce from this, that sec² theta is plus, so how much minus has come here and this minus has gone there, how much plus can we write or we can deduce another condition from this that in place of sec² theta we can also use 1 + tan² theta because this is minus, so how much plus has gone there, if sec² theta is - 1, then what can we write in place of sec² ² theta - 1? tan² theta. So what will be left with me, Babu? sec² became sec².

[00:34:17]And you asked what is its value sir?

[00:34:19]This is tan² theta. Correct? But we had to prove both of them, in which one should we bring them?

[00:34:24]Tan was becoming Eko tan. What was Eko becoming? sec was being made. So can we write sec² in place of theta?

[00:34:34]What can be written in place of 1 + tan² theta and sec²?

[00:34:35]Tan because what we have to prove is that in which both should we bring it? In tan.

[00:34:39]So what will you write in place of this sec² theta, Babu?

[00:34:43]So how much is this 1 plus? tan² theta.

[00:34:46]Now what was already available? If you get it done from tan one then how much will it be? And if we get it integrated with this, then how much power will it have on two tans? 4 Theta arrived.

[00:34:58]I will understand once again sir. It has four dives.

[00:35:01]Two cows were taken out from each of the two cows near it.

[00:35:04]So he must have two left. If it has nothing left then the forest will be left. This is what happened.

[00:35:09]Babu, what is the value of sec² - 1 written in front of you now?

[00:35:14]This is what happened. Babu, what should I write in place of this sec² x? Is tan² correct? And this became sec² of sec². Then take it down.

[00:35:23]What will be the value of sec²?

[00:35:27]So where sec² was, write 1 + tan² and subtract it from x, what will happen? Will you subtract tan² and tan² from tan²? How much is 10 per power? 4 is correct? Should we move ahead?

[00:35:41]See you next.

[00:35:45]These are six cows, Babu. Isn't that it? If we talk about LHS.

[00:35:51]So what is this sin to the power 6 theta and this cos to the power? 6 theta.

[00:35:58]Can we write this thing correctly?

[00:36:04]What is the whole value of sin² theta cos² theta? Did anything happen? did something happen?

[00:36:14]Who is running away?

[00:36:32]You are not reading or listening sir, you guys go ahead and see Babu a - the formula of a + b was written behind also, it was power six Babu, this was power six, so how much six is ​​this to the power, we should write q on the square, this should also be written q on the square, how much six is ​​3 * 2, how much is 3 * 2? Six is ​​correct. Will it become six? Now we will see here, just before we wrote to you that if a plus b formula Babu, what is a + b and what is it in the bracket? a² -ab and plus how much? This is what b² is made of.

[00:38:59]If we talk, what will come in place of a here? What will be made in place of this thing and b? cos, so he told us what to do first, add a + b once, so if we add a + b, what will we write, sir, sin² theta plus cos², will we write this, then what did he say next, Babu, square square, no, he said square, yes we have to make 1 - 3sin² theta, sir, no, it will not be made with this, it will not be made with this.

[00:39:44]Sir, let me also think for a minute.

[00:39:49]Look, pick it up this way, sir. Please pick it up this way, Babu.

[00:40:01]We have a + b = a + b.

[00:40:08]Now, sir, can we write minus as 3a²b and plus as 3ab²? can you write 3ab² sir? Why?

[00:40:22]Look a little carefully. I will prove it sir. If we were to write a + b, then sir, just now the formula of a + b was told, what is the amount of a + b plus 3a²b minus 3ab², and then what is the amount of plus sir 3a²b and what is the amount of plus 3ab², sir, write this thing correctly because if this does not cut both of them, sir, well, if we write a mistake here in the formula, then there will be no plus, sir, this is correct.

[00:41:33]Wait, it is a + b, right Babu, so what have we got Babu, how much is the formula of a + b, we are making a mistake, sir, stop, can we write it like this? Correct? Please listen.

[00:42:32]a + b is done sir. = a - b - 3a²b plus how much is gone? Why 3ab?

[00:42:41]Because a + b is not omitted. Formula of a - b a + b a yes no sir somewhere we are making a mistake sir somewhere we are making a mistake it has come, it will come sir you will see it will come sir you will see it this is what we want sir just now we had made it in the form of q can we write it how much is sin² theta times b plus sir how much is cos² theta times b is correct we know what to write in its place? If you have a + b sir, then in its place you can use a + b - 3 ab and a + b in brackets sir. Because if you calculate both, sir, if you calculate a + b = how much, Babu should write a + b - how much, 3ab and in the bracket a + how much b should not be written, if we talk then what will we write about a plus how much b, a + b plus how much is 3a²b and plus can be said to be 3ab². If we convert minus into minus, it becomes 3a²b. Now how much is the minus? will become 3ab². So we will know this and what will be cut from this, sir, then both q will be equal to q, sir, so here also whatever we put in place of a, Babu, then whom will we put in place of a, this will become a for me and what will become b, so what will we put in place of a, sin² theta, now how much will be in place of b, here also how much will be the minus 3 in place of a, how much will be the sin² theta in place of b and how much will be the sin² theta plus in place of a + b? cos² theta will become this. Let's say the value of sin² theta + cos² theta was not a good cube of one, sir, it became cube of 1 - 3 * how much is this? How much is sin² theta into? What is the value of cos²? Forest. If we make a cube of one then it is one, right?

[00:46:12]How much is the minus? 3sin² theta into how much? cos square theta. And if you get something into one, how much? Forest. You just have to remember this line: if sin to the power of 6 theta is here, and cos to the power of here, what is it? 6 Can we call it a cube of a square? Can this also be called a cube of a square? So a - what do you say, in place of a + b, we have a + b - 3ab and plus what? You can also keep a + b.

[00:46:40]Why? Because when we calculated it, we found that all four were cut. So what will be left from here also a + b, so what will be left from here also a + b, so what will be written in place of a, Babu, sin² theta, what will be written in place of b, cos² three times three, what will be written in place of a, how much will be written in place of sin² theta b, then after that if a a + b was not there then how much sin² theta plus cos, what will be its value, one, if we cube one then it is one, 3 becomes three, the value of sin² theta + cos² theta is also how much, so one becomes one, when we factor it into this then the same thing will be left, so we can say that LHS is equal to RHS, Babu, the value of sin² theta + cos² theta will not be one, so if we factor it into one then the same thing will not be left, hence we will listen to this thing, let us leave it till here, let us move ahead tomorrow and will prepare the page tomorrow, understood, yes, tomorrow we will prepare the page of chart paper