 Hello and welcome to the session. Let's work out the following question. It says prove the following identity Where the angles involved are acute angles for which the expression is defined. Now, let's now move on to the solution and let's start with LHS LHS is cos a upon 1 plus sin a plus 1 plus sin a upon cos a Now we'll simplify LHS and we'll prove that it is equal to RHS. So we take the LCM. So we have cos square a plus 1 plus sin a Whole square in the numerator and in the denominator we have 1 plus sin a into cos a This is again equal to cos square a plus 1 plus sin square sin a whole square will be 1 plus Sin square a they're using the formula of a plus b whole square, which is a square plus b square plus 2 a b So it is 2 into sin a upon 1 plus sin a into cos a Now again, this is equal to cos square a plus sin square a plus 1 plus 2 sin a upon 1 plus sin a into cos a Now we know that cos square a plus sin square a is 1. So it is 1 plus 1 plus 2 sin a upon 1 plus sin a into cos a This is again equal to 2 plus 2 sin a upon 1 plus sin a into cos a Now this is equal to 2 into 1 plus sin a upon 1 plus sin a into cos a taking 2 common 1 plus sin a gets cancelled with 1 up 1 plus sin a and we have 2 upon cos a Now 1 upon cos a is secant a so we have 2 into secant a which is RHS Hence we have proved that LHS is equal to RHS So this completes the question and the session life around take care. Have a good day