# How do you verify the identity cos 4x + cos 2x = 2 - 2 sin^2 2x - 2 sin^2 x?

Use the trig identity: $\cos 2 a = 1 - 2. {\sin}^{2} a$
$\cos 4 x = 1 - 2. {\sin}^{2} \left(2 x\right)$
$\cos 2 x = 1 - 2 {\sin}^{2} \left(x\right)$
$y = \cos 4 x + \cos 2 x = 2 - 2. {\sin}^{2} \left(2 x\right) - 2. {\sin}^{2} \left(x\right)$.