Identidades de Ángulo Doble

\begin{align} \sin 2\alpha &= 2\sin \alpha \cos \alpha = \frac{2\tan \alpha}{1 + \tan^{2} \alpha} \\ \\ \cos 2\alpha &= \cos^{2} \alpha - \sin^{2} \alpha = \frac{1 - \tan^{2} \alpha}{1 + \tan^{2} \alpha} \\ \\ \tan 2\alpha &= \frac{2\tan \alpha}{1 - \tan^{2} \alpha} \\ \\ \cot 2\alpha &= \frac{\cot^{2} \alpha - 1}{2\cot \alpha} \\ \end{align}