数学三角公式

2021-05-29 本文已影响0人晏雪峤_美杜莎

万能公式

$\sin2\alpha =2\sin\alpha \cos\alpha$

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

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

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

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

和差公式
$\sin(\alpha +\beta ) = \sin\alpha \cos\beta + \cos\alpha \sin\beta$

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

$\cos(\alpha + \beta ) = \cos\alpha \cos\beta - \sin\alpha \sin\beta$

$\cos(\alpha - \beta ) = \cos\alpha \cos\beta + \sin\alpha \sin\beta$

$\tan(\alpha + \beta ) = \frac{\tan\alpha + \tan\beta}{1-\tan\alpha \tan\beta }$

$\tan(\alpha - \beta ) = \frac{\tan\alpha - \tan\beta}{1+\tan\alpha \tan\beta }$

$\cot(\alpha + \beta ) = \frac{1-\tan\alpha \tan\beta}{\tan\alpha +\tan\beta}$

$\cot(\alpha - \beta ) = \frac{1 + \tan\alpha \tan\beta}{\tan\alpha - \tan\beta}$

推荐一个好用的编写数学公式的在线 LaTex
LaTexLive