JEE Advanced 2026 Maths Question solved using Basic Trigonometry | How to think like a PRO?

[00:00:00]Hello everyone, in today's video we are going to see a trigonometry question of JEE Advanced 2026.

[00:00:05]See, first of all, as soon as many students hear JEE Advanced, they get scared that the questions will be of very long length or something like that.

[00:00:12]But first of all you have to keep this fear aside. Only then will you be able to attempt the questions correctly and confirm your selection.

[00:00:21]Not every question is that tough.

[00:00:23]Especially, you may find the question lengthy but you see that it has four parts, so it is possible that when you solve each part individually, it may not seem that difficult to you and if you also get some selective questions correct in JEE Advanced, then you can get a good rank and you can get your seat in IIT.

[00:00:40]And here I will tell you some things, I mean if you tell a class 10th student, he will also be able to solve the things to a great extent and if he has some basic knowledge of properties of trigonometry of class 11th also, then this question could have been attempted. Now first of all let us try to solve all its four parts separately. And one more thing is that many times it happens that by taking inspiration from the questions of JEE Advanced, questions are made in your Mains. So, you should also try that you are doing the PYQs of Mains and also attempt some JEE Advanced papers of last 10 years.

[00:01:11]Because look, you will get benefit in JEE Advanced and you will definitely get benefit in Mains also. First of all, look at the number of elements in the set sin to the power of 6x + cos to the power of 4x = 1. This is how the question is framed here. The thing that should come to your mind.

[00:01:25]We used to do such things in class 10th questions also because many times there were proofs or all these things that you should understand here a little carefully.

[00:01:35]Let sin to the power of 6x be on this side. 1 - cos to the power of 4x. What will be the benefit of this? I can open this with a² - b².

[00:01:44]This will become 1 - cos² x and this will become 1 + cos² x Now 1 - cos² x so ours will simply become sin² x. Okay, right? And what was your point here? The power of sin was only 6x.

[00:01:54]So what will you get if this gets cancelled? 4x to the power of sin. Look, the question has been simplified to a great extent here.

[00:02:03]But keep one thing in mind because you had cancelled sin² x here, so sin² x which is 0 here will also be a solution for you.

[00:02:11]That is, sin x = 0 and speaking between -π and π. So what can x be yours? Your x can be -π, 0, and π, all these things because it is given in a close interval.

[00:02:25]Now let us try to find a solution to these.

[00:02:27]So what can we do inside it now?

[00:02:32]If you try to think logically in this, then you do not need to solve it further.

[00:02:36]Otherwise, you can do this one thing.

[00:02:38]Now, I moved sin to the power of 4x here and wrote cos² x here, so I tried to open 1 - sin to the power of 4x in the same way.

[00:02:44]But even in that, some steps will be longer. If we use our brain a little here, then one thing can be understood that brother, from where to where does our sin x extend? It ranges from -1 to one. Now because his power has become even here.

[00:02:56]So how far has this thing reached you? This value is going to remain between 0 to 1. Are you understanding this thing? And what remains of our cos x here? -1 remains one. But again, if it's squared, it's going to be zero to one.

[00:03:08]Meaning, where will this total quantity of yours last? It is going to be between one and two.

[00:03:12]Now the left hand side is between zero and one.

[00:03:14]This is between one and two.

[00:03:16]So there is only one possibility that all your values ​​become equal to one here. Isn't it? 4x to the power of sin becomes one and 1 + cos² x also becomes equal to 1. So cos² x 0 and cos² x 0 means sin to the power of 4x = 1, right? It's the same thing in a way. So here you will get the solution that brother, our sin² x can be one and sin² x here can also be -1.

[00:03:43]Now this solution is not possible. Because a perfect square will never be -1. So if we talk about sin² x = 1, then it means that our sin x can be one and our sin x here can also be -1. Now, if we look carefully at the solutions for this, your x = will be at π / 2. And this one will be at x = -π / 2. So how many solutions did we get in total?

[00:04:07]Five solutions were found. And to validate it once, you can enter these and check whether it is coming correctly or not. So if I put sin π / 2 here, it becomes one. This will become your zero. Are getting. Isn't it? If I put in -π/2, you get what's here. And at -π 0 and π, brother, it is clear that this quantity will become zero. This will become a forest.

[00:04:24]So these are also the right solutions for you.

[00:04:26]So there will be five solutions. So what will be your answer to P? There will be five.

[00:04:31]Meaning option B. Now there will be only one answer from option B and C. Isn't it?

[00:04:35]So brother, half of your options have been eliminated. It turns out that we do n't even need to solve the entire question. Next, look here sin² x + cos power 6x = 1 again. After looking at the first one, you understood what strategy you are going to use. Please send this term here. cos to the power of 6x equal to what will this become for you? cos² will become x. So if I cancel here, cos to the power 4x = 1 is coming out and at the same time cos² x which is yours becomes equal to 0.

[00:05:00]Meaning that cos x = 0, so when is this possible? It's possible for this to be either -π/2 or π/2. So you have got these two solutions. Now what could be the solution to this? cos² x becomes one and cos² x becomes -1.

[00:05:15]So that -1 is not possible. So leave him. In this also, two things are possible for you, that your cos x becomes one and cos x becomes -1. -1 When do we live? Here it resides at π.

[00:05:26]Now that is not within this domain. So, no solution will be found for this here. And if I talk about cos x = 1, then it can be found at x = 0 which will bring it in between. So you have a total of three solutions here. If you want to check it again by putting it in, you can check it.

[00:05:40]So what is here will become zero and here yours will become one. When x = 0 we put Similarly, if you enter -π / 2 and enter π / 2, this will become your zero. And what will you find here? You will find the forest. Because what is there here? Square is installed. So even on minus it will give you positive value.

[00:05:54]So there should be a total of three solutions here.

[00:05:56]Meaning, what will be your answer to q? It will remain three. So there is only one option. That means option B is your correct answer.

[00:06:04]So then you did not need to solve any further because brother, only one question was asked here in single choice.

[00:06:10]Still, if you want to take the test here as a practice, then let us take a look at the further questions also.

[00:06:16]cos² x/2 - sin² x = 1/2 So what do you have to do here? Now this one is a half angle and here yours is a double angle. So we should understand this thing that you will have to apply the identity of 2 theta.

[00:06:30]Which one will have to be installed? So for that, if you multiply these two here, then you will start seeing more things clearly. Isn't it? This becomes 2sin² x = 1. Now, call the one over here on this side and send 2sin² x over there. So what has happened to us? 2 cos² theta - 1 which becomes our cos 2 theta. So, this will be your cos x and what is this, 2sin² x, so write it as 1 - cos² x. Now brother, the quadratic equation is being formed directly in terms of cos, so there is no need to take any more tension, your answer will come here.

[00:07:03]Ok? So what will be the value of cos x here? Your -1 + - b² b² means 1 - 4ac so 4 * 2 * 2 means your 16 becomes 2ac so this becomes 4 so -1 + - 17 / 4 is coming. Now see, 17 which is 4 something will be the value here.

[00:07:26]So -1 and -4 cannot be something because then it would be a value smaller than -1.

[00:07:32]Whereas your cos remains between -1 to 1.

[00:07:34]So ignore the minus one.

[00:07:36]Plus one is possible. So 17 is your -1/4, this is the value of cos x.

[00:07:42]Now we are talking about -pi / -π to π.

[00:07:46]So look at a little graph of cos here.

[00:07:48]What will our cos graph look like? Here, in this way you have reached zero and here, in this way you will see π. Similarly, for -π, you will see it something like this. Now here we are getting some positive value. Ok? If your problem is smaller than one, then suppose you are getting it somewhere here, then how many total solutions can be possible for it? Only two solutions are possible. So which option will be correct for you? Whatever is of R should be second. Look brother, it is coming in the same option.

[00:08:18]Absolutely correct. Isn't it? Next, let's see the last part here. 6 sin² x/2 - cos 3x = 3 Now if I leave - cos 3x here and send this three term over there and take the three common, what will this become for us? 1 - 2sin² x / 2 means 1 - 2sin² theta which is = cos 2 theta so what will this become for you? 3 * cos x, right? And what is there here? - cos is 3x.

[00:08:48]Now what is our cos 3x equal to? 4 cos x - 3 cos x, right? So when there is a negative here, what will happen to you? 3 cos x - 4 cos x = 3 cos x Now we can cancel this out here.

[00:09:06]Okay, don't put it equal to zero, brother, when we cancel it in multiplication because it is as a factor, hence we put it equal to 0. Here, your addition and subtraction have been given, so there is no tension. Isn't it? So what answer will we get from here that 4 cos x = 0, that is, what will happen to your cos x? = 0 means cos x = 0, so now what will be the number of solutions here? So what can you put in x? If we talk about zero here, then if your total is from 2π to this, then you can again use the graph. Isn't it? So in this way, what did you get here? The pie came. And this is yours, 2π will come here. Similarly, this 2π here will come. So how much is Zero cutting now? 1 2 3 and 4. So in total, four solutions are possible here.

[00:09:55]So what is the option here? The S will be four here. Look brother, that also fits you perfectly. Then it means that option B is the correct answer. So brother, keeping a little patience, whatever problems you have seen here can also be asked individually in the mains. Isn't it? And if we count them, then they are being asked at the Easy level only. There were no such tough people. So trigonometry is not that tough. You should target that if a question of trigonometry or inverse trigonometry is being asked then you should attempt it under any circumstances and it is not that it is too much mixed with other chapters. It has its own individual properties and identities.

[00:10:31]So work hard and definitely you can crack JE well. If you haven't subscribed to the other channels, please do so. Because the more you practice maths here, the better you will feel in maths and here on the channel you will get to see a lot of practice.

[00:10:46]You are practicing what you have in shorts.

[00:10:48]Even in the long term, I will bring continuous question solving sessions, so you will get to practice very well. Let's meet in the next video. Till then take care and goodbye.

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