Tangens — qarşı katetin qonşu katetə olan nisbətinə deyilir. İfadəsi: tan ⁡ α = | B C | | A B | = sin ⁡ α cos ⁡ α = 1 cot ⁡ α {\displaystyle \tan \alpha ={\frac

${\displaystyle \tan(90-\alpha )=\tan \alpha }$

${\displaystyle \tan(90+\alpha )=-\cot \alpha }$

${\displaystyle \tan(180-\alpha )=-\tan \alpha }$

${\displaystyle \tan(180+\alpha )=\tan \alpha }$

${\displaystyle \tan(270-\alpha )=\cot \alpha }$

${\displaystyle \tan(270+\alpha )=-\cot \alpha }$

${\displaystyle \tan(360-\alpha )=-\tan \alpha }$

${\displaystyle \tan(360+\alpha )=\tan \alpha }$

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

${\displaystyle \tan 3\alpha ={\frac {3\tan \alpha -\tan ^{3}\alpha }{1-3\tan ^{2}\alpha }}}$

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

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

${\displaystyle \tan \alpha +\tan \beta ={\frac {\sin(\alpha +\beta )}{\cos \alpha *\cos \beta }}}$

${\displaystyle \tan \alpha -\tan \beta ={\frac {\sin(\alpha -\beta )}{\cos \alpha *\cos \beta }}}$