These formulae are often refered to as the addition formulae:

\sin(A \pm B) = \sin A \cos B \pm \cos A \sin B

\cos(A \pm B) = \cos A \cos B \mp \sin A \sin B

\tan(A \pm B) = \displaystyle \frac{\tan A \pm \tan B}{1 \mp \tan A \tan B}

\sin(A \pm B) = \sin A \cos B \pm \cos A \sin B

\cos(A \pm B) = \cos A \cos B \mp \sin A \sin B

\tan(A \pm B) = \displaystyle \frac{\tan A \pm \tan B}{1 \mp \tan A \tan B}