Prove the Identity $$\cos ^ { 4 } x = \frac { 1 } { 8 } ( 3 + 4 \cos 2 x + \cos 4 x )$$

Prove the identity.
- $$\cos ^ { 4 } x = \frac { 1 } { 8 } ( 3 + 4 \cos 2 x + \cos 4 x )$$