Double Angle Question W/Picture. Attached
Use the Pythagorean Identity to simplify the double angle identity you've been given so far...
$\displaystyle \displaystyle \begin{align*} \sin^2{(x)} + \cos^2{(x)} \equiv 1 \end{align*}$, so that means
$\displaystyle \displaystyle \begin{align*} \cos{(2x)} &\equiv \cos^2{(x)} - \sin^2{(x)} \\ &\equiv 2\cos^2{(x)} - 1 \\ &\equiv 1 - 2\sin^2{(x)} \end{align*}$