Verify the identity.

cos 4u = cos22u - sin22u

To verify the above we proceed as follows:

cos 2u = (cos u) ^2 - (sin u) ^2

hence,

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

By Pythagorean identity:

(sin 2u) ^2 + (cos 2u) ^2=1

thus;

(sin 2u) ^2=1 - (cos 2u) ^2

hence

(cos 2u) ^2 - (1 - (cos 2u) ^2)

= (cos 2u) ^2-1 + (cos u) ^2

2 (cos 2u) ^2-1

=cos (4u)