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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}