$$\begin{eqnarray*} \sin\left(A+B\right) & = & \sin A\cos B+\sin B\cos A\\ \sin\left(A-B\right) & = & \sin A\cos B-\sin B\cos A\\ \cos\left(A+B\right) & = & \cos A\cos B-\sin A\sin B\\ \cos\left(A-B\right) & = & \cos A\cos B+\sin A\sin B\\ \tan(A + B) &=& \frac{\tan A + \tan B}{1 - \tan A \tan B}\\ \tan(A - B) &=& \frac{\tan A - \tan B}{1 + \tan A \tan B} \end{eqnarray*}$$