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

$\sin (u\pm v)=\sin u\cos v\pm \cos u\sin v$

$\cos (u\pm v)=\cos u\cos v\pm \sin u\sin v$

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