 Hello friends welcome to another problem-solving session in this Session we are going to prove another trigonometric identity So if you can see that identity given is cost to the power 4 theta minus sign to the power 4 theta plus 1 is equal to 2 cos square theta Now after looking at such problems, what should come to your mind first? So if you can see there is a power 4 over there and there's a minus sign between the two ratios Right cost to the power 4 theta minus sign to the power 4 theta Now many times many students find this to be intimidating this power to be intimidating and they you know skip the question But actually it is very straightforward the moment you see such powers You know that it is a case of algebraic identities. You have to use algebraic identities and using them in Association with let us say the trigonometric ratios and trigonometric identities. You can solve this problem So the moment I see a power 4. I know power 4 is nothing but square of square So if you see LHS can be written as cos of Squared cos square theta square. This is cost to the power 4, right? And why am I reducing it to square because I know some relationships Which involves cos square and sine square theta now the second term also is now the second term also is sine square theta So sine square theta whole square, isn't it? Right, and then there's a plus one which is there in the problem now If you see the first two terms here are of the form of a square minus b square, isn't it? And this is algebraic identity. I was talking about so this is nothing but a minus b times a plus b So we are going to use this identity here. So hence the LHS will become cos square theta minus sine square theta This is the first factor and the second factor is cos square theta Plus sine square theta Please don't get confused because it is square of square So hence my a here is if you look closely a is nothing but cos of square theta not cos theta, right? Because there's a square on cos square as well and b is what? Sine square theta. So using this I I can write like this, isn't it? Now again, we know one of the identities basic identities trigonometric identities We learned is cos square theta plus sine square theta is 1 so our job here if you notice This particular factor will be reduced to 1 so hence what do I get? I get cos square theta minus sine square theta multiplied by 1 will give you this only and then plus 1 Now again using the same identity you can so always keep a track of what is to be you know To be proven that is where do you want to go? That means what is RHS? So this is my RHS. I want to achieve 2 cos square theta So if you can see one cos square theta is already there So you want one more and if you notice carefully This is the another cos square theta from This identity why because cos square theta can be represented as 1 minus sine square Theta, so hence using that identity. I Can write don't put this This sign this is equal to so this is equal to equal to and hence equal to cos square theta cos square theta Plus another cos square theta, isn't it? Which is equal to 2 cos square theta, which is equal to RHS This is what the problem was demanding So what is the learning? Learning is do not get panicked by seeing higher powers whenever there is a higher power. It is exact It is actually very easy problem because You know that there is an algebraic identity, which is going to be used They can also give you identities or you know problems where there is something like cos to the power 6 theta Minus sine to the power 6 theta So again, you know if there is a there is a problem involving this kind of a term Then you know what to do. You have you know that this is nothing but a square cube Minus b square cube is nothing but a to the power 6 minus b to the power 6 So basically you have to reduce this into this form Correct, and now you can use the identity a cube minus b cube is what a minus b a square plus a b plus B square and hence proceed like that Hence always keep in mind that the moment there are higher powers, you know that algebraic identity is going to be used in that problem