$\cos 2 \alpha =$ $1 -$ $2 \sin ^{2} \alpha$
$\cos 2 \alpha =$ $\cos ^{2} \alpha -$ $\sin ^{2} \alpha$
$\sin 2 \alpha =$ $2 \sin \alpha \cos \alpha$
$1 +$ $\cot ^{2} \alpha =$ $\csc ^{2} \alpha$
$1 +$ $\tan ^{2} \alpha =$ $\sec ^{2} \alpha$
$\sin ^{2} \alpha +$ $\cos ^{2} \alpha =$ $1$
$\cot \alpha =$ $\frac{\cos \alpha}{\sin \alpha}$
$\tan \alpha =$ $\frac{\sin \alpha}{\cos \alpha}$
$\begin{cases} & \tan \alpha \cdot \cot \alpha = 1; \\ & \sin \alpha \cdot \csc \alpha = 1; \\ & \cos \alpha \cdot \sec \alpha = 1. \end{cases}$
$\csc A =$ $\frac{b}{a}$
$\sec A =$ $\frac{b}{c}$
$\cot A =$ $\frac{c}{a}$
$\tan A =$ $\frac{a}{c}$
$\cos A =$ $\frac{c}{b}$
$\sin A =$ $\frac{a}{b}$
