Compound Angle Identity

Sine

$\sin (A+B)\equiv \sin (A)\cos (B)+\cos (A)\sin (B)$

Cos

$\cos (A+B)\equiv \cos (A)\cos (B)-\sin (A)\sin (B)$

Tan

$\tan (A+B)=\frac{\tan (A)+\tan (B)}{1+\tan (A)\tan (B)}$