Тригонометриялық формулалар

$\sin\left(\alpha+\beta\right)=\sin\alpha\cos\beta+\cos\alpha\sin\beta$

$\sin\left(\alpha+\beta\right)=\sin\alpha\sin\beta+\cos\alpha\cos\beta$

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

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

$tg\left(\alpha-\beta\right)=\frac{tg\beta-tg\alpha}{1-tg\alpha tg\beta}$

$tg\left(\alpha-\beta\right)=\frac{tg\alpha-tg\beta}{1+tg\alpha tg\beta}$

$tg\left(\alpha-\beta\right)=\frac{tg\alpha-tg\beta}{1-tg\alpha tg\beta}$

$tg\left(\alpha-\beta\right)=\frac{tg\alpha-tg\beta}{tg\alpha tg\beta-1}$

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

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

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

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

$\operatorname{ctg}\left(\alpha+\beta\right)=\frac{1-tg\alpha tg\beta}{tg\alpha+tg\beta}$

$\operatorname{ctg}\left(\alpha+\beta\right)=\frac{1+tg\alpha tg\beta}{tg\alpha+tg\beta}$

$\operatorname{ctg}\left(\alpha+\beta\right)=\frac{1-tg\alpha tg\beta}{tg\alpha-tg\beta}$

$\operatorname{ctg}\left(\alpha+\beta\right)=\frac{1+tg\alpha tg\beta}{tg\alpha+tg\beta}$

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

$\cos\left(\alpha+\beta\right)=\cos\alpha\sin\beta+\sin\alpha\cos\beta$

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

$\cos\left(\alpha+\beta\right)=\cos\alpha\cos\beta+\sin\alpha\sin\beta$

 $\cos^2\alpha+\sin^2\alpha$  

 $\sin\alpha\cos\beta+\cos\alpha\sin\beta$  

 $1-\cos^2\alpha$  

 $2\sin\alpha\cos\alpha$  

 $1-2\sin^2\alpha$  

 $\cos^2\alpha+\sin^2\alpha$  

 $\cos\alpha\cos\beta+\sin\alpha\sin\beta$  

 $\cos^2\alpha-1$  

 $\sqrt{\frac{1+\cos\alpha}{2}}$  

 $\sqrt{\frac{1-\cos\alpha}{2}}$  

 $\sqrt{\frac{1-\cos\alpha}{1+\cos\alpha}}$  

 $\frac{\sqrt{3}}{3}$  

 $2\cos\ \frac{\alpha+\beta}{2}\sin\ \frac{\alpha-\beta}{2}$  

 $2\sin\ \frac{\alpha+\beta}{2}\cos\ \frac{\alpha-\beta}{2}$  

 $-2\sin\ \frac{\alpha+\beta}{2}\sin\ \frac{\alpha-\beta}{2}$  

 $\frac{\sin\left(\alpha-\beta\right)}{\cos\alpha\cos\beta}$  

 $\cos\alpha\cos\beta+\sin\alpha\sin\beta$  

 $\sin\alpha\cos\beta+\cos\alpha\sin\beta$  

 $-2\sin\ \frac{\alpha-\beta}{2}\sin\ \frac{\alpha-\beta}{2}$  

 $2\cos\ \frac{\alpha+\beta}{2}\cos\ \frac{\alpha-\beta}{2}$