Question

Prove the identity.
cos4u=(cos^2)(2u)-(sin^2)(2u)

Answer 1

\[
\cos(4u) = \cos ( 2 u + 2 u)= \cos(2u) \cos(2u)- \sin(2u) \sin(2u)
\]

Answer 2

We use the formula
cos(a+b) = cos(a) cos(b) - sin(a)sin(u)