sin(4x)/sin(x)=4cos(x)cos(x)

Question

verify the identity

Answer 1

sin 4 x = 2 sin 2x cos 2x
= 2 (2 sin x cos x)(2cos^2 x - 1)
= 4 sin x (2cos^2 x - 1) cos x

now identity
4 (2cos^2 x - 1) cos x =?4cos^2x
(2cos^2 x -1) = cos x ??
Perhaps I am missing something?

Answer 2

It is important that the question be copied correctly, whether for posts or for exams.

The question should read:

sin(4x)/sin(x)=4cos(x)cos(2x)

Reduce each side to cos(x) and the identity will be obvious.