 Hi and welcome to the session. I am Asha and I am going to help you with the following version which says, proof the following, cos 4x is equal to 1 minus 8 sin square x into cos square x. So let us begin with the solution and we will start with the left-hand side of the problem and show that it is equal to 1 minus 8 sin square x into cos square x. So left-hand side is cos 4x which can be written as cos 2 lines of 2x which is equal to 1 minus 2 sin square 2x since cos 2a is equal to 1 minus 2 sin square a and here in the place of a we have 2x. So in applying this identity which is identity 14 of your book we get 1 minus 2 sin square a that is 2x. Now this is further equal to 1 minus 2 sin 2x whole square which is equal to 1 minus 2 sin 2x is 2 sin x cos x whole square and this is because sin 2a is equal to 2 sin a into cos a which is identity 15 of your book. So in further simplifying it we have 1 minus 2 2 sin x cos x whole square is 4 sin square x into cos square x which is further equal to 1 minus 8 sin square x into cos square x and this is the right-hand side of the given problem hence we have cos 4x is equal to 1 minus 8 sin square x into cos square x hence proved. So this completes the session hope you enjoyed it take care and bye for now.