Verify the identity: sin 4x = 2 sin 2x cos 2x

Sin 2x = 2 sin x cos x

that is one of the double angle formulas

4x = sin 2 (2x)

then it immediately follows that

sin 2 (2x) = 2 sin 2x cos 2x

Verify the identity: sin 4x = 2 sin 2x cos 2x

We use a trigonometric identity as follows:

sin (a+b) = sin (a) cos (b) + cos (a) (sin (b)

We s tart with

sin (4x) = sin (2x+2x)

sin (2x+2x) = sin (2x) * cos (2x) + cos (2x) * sin (2x)

Then, it will simplify to

2sin (2x) cos (2x)

Hope this answers the question.