Question

Verify the identity:

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

My work:
cos(4x) = 2(cos^2 x) - (sin^2 x)
cos(4x) = 2((1 + cos 2x)/2 - (1 - cos 2x)/2)
cos(4x) = 2 cos(4x)/2
cos(4x) = cos(4x)

Is this correct? It seems too simple.

Answer 1

Yeah.

Answer 2

There's more than one way to do it.

Answer 3

when given to veirfy
substitute values instead of x