High School Trigonometry/Sum and Difference Identities for Sine and Tangent

$$\sin{(u \pm v)} = \sin{u}\cos{v} \pm \cos{u}\sin{v}$$ $$\cos{(u \pm v)} = \cos{u}\cos{v} \pm \sin{u}\sin{v}$$ $$\tan{(u \pm v)} = \frac{\tan{u} \pm \tan{v}}{1 \pm \tan{u}\tan{v}}$$