Double Angle Identities

 \sin(2\theta) = 2\sin\theta\cos\theta


\begin{matrix}
\cos(2\theta) = \cos^2\theta - \sin^2\theta\\
= 1 - 2sin^2\theta\\
= 2cos^2\theta - 1\\
\end{matrix}

 \tan(2\theta) = \dfrac{2\tan\theta}{1-\tan^2\theta}