4 sin ( 2 x ) cos ( 2 x )

Question

how do I write as a single identity

Answer 1

Use the identity

sin(2y) = 2 siny cosy

4 sin(2x) cos(2x) = 2 [2 sin(2x) cos(2x)] = 2 sin[2(2x)] = 2 sin(4x)