High School Trigonometry/Double-Angle Identities

$$\sin{2u} = 2\sin{u}\cos{u}$$ $$\begin{aligned} \cos{2u} &= \cos^{2}{u} - \sin^{2}{u} \\ &= 2\cos^{2}{u} - 1 \\ &= 1 - 2\sin^{2}{u} \end{aligned}$$ $$\tan{2u} = \frac{2\tan{u}}{1 - \tan^{2}{u}}$$