1 + \operatorname{cot}^2 x & = \operatorname{cosec}^2 x, \quad \text{where } \sin x \ne 0 \\
1 + \tan^2 x & = \operatorname{sec}^2 x, \quad \text{where } \cos x \ne 0
\end{split}\end{equation}
+
+## Compound angle formulas
+
+$$\cos(x \pm y) = \cos x + \cos y \mp \sin x \sin y$$
+$$\sin(x \pm y) = \sin x \cos y \pm \cos x \sin y$$
+$$\tan(x \pm y) = {{\tan x \pm \tan y} \over {1 \mp \tan x \tan y}}$$
+
+## Double angle formulas
+
+\begin{equation}\begin{split}
+ \cos 2x = \cos^2 x = \sin^2 x
+\end{split}\end{equation}
+
+$$\sin 2x = 2 \sin x \cos x$$
+
+$$\tan 2x = {{2 \tan x} \over {1 - \tan^2 x}}$$
+