 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, sin x minus sin 3x upon sin square x minus cos square x is equal to 2 sin 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 2 sin x. So left hand side is sin x minus sin 3x upon sin square x minus cos square x. First let us learn some simple identities with say sin a minus sin b is equal to 2 cos a plus b upon 2 into sin a minus b upon 2 which is identity 20 of your book. The second identity is cos square x minus sin square x is equal to cos 2x and this is identity 14 of book. Now we are using these two identities. LHS can further be written as sin x minus sin 3x within the form of sin a minus sin b. So 2 cos a plus b a is x and b is 3x. So we have 4x upon 2 into sin a minus b. So a is x and b is 3x. So x minus 3x is minus 2x upon 2 and in the denominator we have sin square x minus cos square x which on a plan the second identity can be written as minus cos 2x which is further equal to 2 cos 2x into sin of minus x upon minus cos 2x. Now sin of minus x can be written as minus sin x so we have minus 2 cos 2x into sin x upon minus cos 2x minus minus cancels out cos 2x with cos 2x we are left with 2 sin x which is the right hand side of the given problem and hence we can say that sin x minus sin 3x upon sin square x minus cos square x is equal to 2 sin x hence proved. So this completes the solution hope you enjoyed it take care and have a good day.