标签： 高等数学基础

$\sin (\alpha \pm \beta )=$ $\sin \alpha \cos \beta$ $\pm$ $\cos \alpha \sin \beta$

${\cos }^2\alpha =$ $\frac{1+\cos 2\alpha }{2}$

$\cot 2\alpha =$ $\frac{{\cot }^2\alpha –1}{2\cot \alpha }$

$\tan 2\alpha =$ $\frac{2\tan \alpha }{1–{\tan }^2\alpha }$

${\sin }^2\alpha =$ $\frac{1–\cos 2\alpha }{2}$

$\cos 2\alpha =$ $2{\cos }^2\alpha -$ $1$

$\cos 2\alpha =$ $1-$ $2{\sin }^2\alpha$

$\cos 2\alpha =$ ${\cos }^2\alpha -$ ${\sin }^2\alpha$

$\sin 2\alpha =$ $2\sin \alpha \cos \alpha$

$1+$ ${\cot }^2\alpha =$ ${\csc }^2\alpha$

$1+$ ${\tan }^2\alpha =$ ${\sec }^2\alpha$

${\sin }^2\alpha +$ ${\cos }^2\alpha =$ $1$

$\cot \alpha =$ $\frac{\cos \alpha }{\sin \alpha }$

$\tan \alpha =$ $\frac{\sin \alpha }{\cos \alpha }$

$\{\begin{array}{ll}& \tan \alpha \cdot \cot \alpha =1;\\ & \sin \alpha \cdot \csc \alpha =1;\\ & \cos \alpha \cdot \sec \alpha =1.\end{array}$