Question

Verify the identity, cos 4u = cos^2(2)u - sin^2(2)u

Answer 1

$\bf \textit{Double Angle Identities} \\ \quad \\ sin(2\theta)=2sin(\theta)cos(\theta) \\\\ \quad \\ cos(2\theta)= \begin{cases} \boxed{cos^2(\theta)-sin^2(\theta)}\\ 1-2sin^2(\theta)\\ 2cos^2(\theta)-1 \end{cases} \\ \quad \\\\ tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)}\\\\ -------------------------------\\\\ cos(4u)=cos^2(2u)-sin^2(2u) \\\\\\ cos^2(2u)-sin^2(2u)\implies cos[~~2~(2u)~~]\implies cos(4u)$