 Hello and welcome to the session. In this session we are going to discuss the following question which says that prove that cotton wool sauce 1 plus sine next upon cos x is equal to pi by 4 minus x by 2. We know that sine os 2 theta is equal to 2 sine theta cos theta and 2 cos theta is equal to 1 plus cos 2 theta. With this key idea we shall proceed with the solution. We need to prove that cotton wool sauce 1 plus by cos x is equal to pi by 4 minus x by 2. On the right hand side we have cotton wool sauce 1 plus sine x whole upon cos x which can be written as cotton wool sauce 1 plus cos of pi by 2 minus x whole upon 1 by 2 minus x is equal to sine of x and sine of pi by 2 minus x is equal to cos x. From the key idea we know that 2 cos square theta is equal to 1 plus cos 2 theta. Now 2 cos square theta is given by 1 plus cos 2 theta. If we assume pi by 2 minus x as 2 theta then 1 plus cos pi by 2 minus x can be written as 2 cos square of pi by 4 minus x by 2. So we have cotton wool sauce 2 cos square of pi by 4 minus x by 2 whole upon 2 theta is given by 2 sine theta cos theta. That is if we assume pi by 2 minus x as 2 theta then sine of pi by 2 minus x can be written as 2 sine of pi by 4 minus x by 2 into cos of pi by 4 minus x by 2. That is 2 sine of pi by 4 minus x by 2 into cos of pi by 4 minus x by 2. Therefore we get cotton wool sauce cos of pi by 4 minus x by 2 upon pi by 4 minus x by 2 which can be written as cotton wool sauce cos of pi by 4 minus x by 2 which is equal to pi by 4 minus x by 2 which is equal to the right hand side plus the result that is cotton wool sauce 1 plus sine of pi by cos x is equal to pi by 4 minus x by 2. This completes our session hope you enjoyed this session.