\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*}