Sum and Difference of Two Angles

\begin{align} \sin (\alpha \pm \beta) &=\sin \alpha\cos \beta \pm \sin \beta\cos \alpha \\ \\ \cos (\alpha \pm \beta) &=\cos \alpha\cos \beta \mp \sin \alpha\sin \beta \\ \\ \tan (\alpha \pm \beta) &=\frac{\tan \alpha \pm \tan \beta}{1 \mp \tan \alpha \tan \beta} \\ \\ \cot (\alpha \pm \beta) &=\frac{\cot \alpha \cot \beta \mp 1}{\cot \beta \pm \cot \alpha} \\ \end{align}