 Hi and welcome to the session. I am Asha and I am going to help you with the following question which says Prove the following, sin square 6x minus sin square 4x is equal to sin 2x into sin 10x. So let us begin with the solution and we will solve the left hand side of the problem and show that it is equal to sin 2x into sin 10x. So left hand side is sin square 6x minus sin square 4x. Now this is in the form of a square minus b square whose formula is a minus b into a plus b. Thus this can further be written as sin 6x minus sin 4x into sin 6x plus sin 4x. Now let us learn two identities with the help of which we will solve. First is sin a minus sin b is equal to 2 cos a plus b upon 2 into sin a minus b upon 2. And second is sin a plus sin b is equal to 2 sin a plus b upon 2 into cos a minus b upon 2. So with the help of these two identities LHS can further written as a plus b are a 6x and b is 4x to 6x plus 4x divided by 2 into sin 6x minus 4x divided by 2. Now opening the second bracket which is sin 6x plus sin 4x it can be written as 2 sin 6x plus 4x upon 2 into cos 6x minus 4x upon 2. This is further equal to 2 cos this is 10x upon 2 is 5x into sin 6x minus 4x is 2x and 2x divided by 2 is x. Now solve the second problem which is 2 sin 5x into cos x. Now this is in the form of 2 a into sin a whose formula is sin 2a. So we can write it as 2 cos 5x taking this 5x here that is we are rearranging these terms such that we get it in the form of 2 cos a into sin a and here 2 sin x into cos x. Now applying this formula now here a is 5x so it can be written as sin 2 into 5x and this bracket can be written as sin 2 into x which is equal to sin 10x into sin 2x which is the right hand side. Hence we can say that sin square 6x minus sin square 4x is equal to sin 2x into sin 10x hence proved. So this completes the solution hope you enjoyed it take care and have a good day.