Verify this identity, step by step. sin 2x= -2sin(x-pi/2)cos(x-pi/2)

Refresh if you see weird display errors.for the left hand side, sine double angle identity can be used:     for the right hand side, we have    i will deal with  separately. we can use this sine difference identity:     from unit circle, etc, we have  , therefore    now i will deal with  separately. we can use this cosine difference  identity:     bringing these two simplifications together:    

Exponential function