 Hi and welcome to the session. I am Asha and I am going to help you with the following question which says proof the following cos pi plus x into cos of minus x upon sin pi minus x into cos pi by 2 plus x is equal to cot square x. So, let us start with the solution and we will solve the left hand side of this problem and show that it is equal to the right hand side. So, left hand side is cos pi plus x into cos of minus x upon sin pi minus x into cos pi upon 2 plus x. So, first let us learn some simple identities which says cos pi plus x is equal to minus cos x second is cos pi by 2 plus x is equal to minus sin x then sin pi minus x is equal to sin x and cos of minus x is equal to cos x. So, the LHS can further be written as by using these identities cos pi plus x is minus cos x cos of minus x is cos x upon sin pi minus x is sin x and cos pi by 2 plus x is minus sin x. So, we have minus 2 times cos inverse cos square x and in the denominator again we have minus sin x into sin x is minus sin square x minus minus cancels out and we have cos x upon sin x whole square and cos x upon sin x is cot x. So, we have cot x whole square which is equal to cot square x and which is the right hand side of the problem and thus we have cos pi minus x into cos of minus x upon sin pi minus x into cos of pi by 2 plus x is equal to cot square x hence proved. So, this completes the solution hope you enjoyed it take care and have a good day.