Основные тригонометрические тождества

$\sin\alpha+\cos\alpha=1$

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

$\sin^2\alpha+\cos^2\beta=1$

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

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

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

$tg\alpha=\frac{1}{\operatorname{ctg}\alpha}$

$tg\alpha=1-\operatorname{ctg}\alpha$

$\operatorname{ctg}\alpha=\frac{\sin\alpha}{\cos\alpha}$

$\operatorname{ctg}\alpha=\frac{\cos\alpha}{\sin\alpha}$

$\operatorname{ctg}\alpha=\frac{1}{\operatorname{ctg}\alpha}$

$\operatorname{ctg}\alpha=\sqrt{1-tg\alpha}$

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

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

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

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

$tg\ \alpha\cdot\operatorname{ctg}\alpha=1$

$tg\ \alpha+\operatorname{ctg}\alpha=1$

$tg^2\ \alpha+\operatorname{ctg}^2\alpha=1$

$tg^2\ \alpha\cdot\operatorname{ctg}\alpha=1$

 $\cos^2\alpha$  

 $1-\sin^2\alpha$  

 $\sin^2\alpha$  

 $0$  

 $\sin\alpha$  

 $\cos\alpha$  

 $\operatorname{ctg}\alpha$  

 $tg\alpha$  

 $\sin^2\alpha$  

 $\cos^2\alpha$  

 $\operatorname{ctg}^2\alpha$  

 $tg^2\alpha$