 Hello and welcome to the session. I am Asha and I am going to help you with the following question that says proof that sin 2x plus 2 sin 4x plus sin 6x is equal to 4 cos square x into sin 4x. Let us now start with the solution. We will start with the left hand side which is equal to sin 2x plus 2 sin 4x plus sin 6x and show that it is equal to the right hand side which can be written as sin 2x plus sin 6x plus 2 sin 4x but we are using the terms and now since sin a plus sin b is equal to 2 sin a plus b upon 2 into cos a minus b upon 2 therefore applying this formula on sin 2x plus sin 6x this statement can further be written as 2 sin a plus b a is 2x and b is 6x so we have a takes upon 2 into cos a minus b so a is 2x minus 6x minus 4x upon 2 plus 2 sin 4x this is further equal to 2 sin 4x into cos 2x plus 2 sin 4x which is further equal to 2 sin 4x into cos 2x since cos of minus theta is equal to cos theta and here we have cos minus 2x so this is equal to cos 2x plus 2 sin 4x and now let us take 2 sin 4x common so we have cos 2x plus 1 this is further equal to 2 sin 4x into cos 2x plus 1 is equal to 2 cos square x since cos square x is equal to 1 plus cos 2x upon 2 which is further equal to 4 sin 4x into cos square x or 4 cos square x into sin 4x which is equal to the right hand side and thus we have the left hand side is equal to the right hand side that is sin 2x plus 2 sin 4x plus sin 6x is equal to 4 cos square x into sin 4x hence proved so this completes the solution take care and good bye for now.