формули подвійного, потрійного та половинного кутів

$$\sin (2\alpha )=2\sin (\alpha )\times \cos (\alpha )$$

$$\cos (2\alpha )={\cos }^2(\alpha )-si{n}^2(\alpha )$$

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

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

$$tg(2\alpha )=\frac{2tg(\alpha )}{1-t{g}^2(\alpha )}$$

$$ctg(2\alpha )=\frac{1-t{g}^2(\alpha )}{2tg(\alpha )}$$

$$\sin (3\alpha )=3\sin (\alpha )-4{\sin }^3(\alpha )$$

$$\cos (3\alpha )=4{\cos }^3(\alpha )-3\cos (\alpha )$$

$$tg(3\alpha )=\frac{\sin (3\alpha )}{\cos (3\alpha )}$$

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

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

$$t{g}^2(\frac{\alpha }{2})=\frac{1-\cos (\alpha )}{1+\cos (\alpha )}$$

$$tg(\frac{\alpha }{2})=\frac{1-\cos (\alpha )}{\sin (\alpha )},\alpha \ne \pi n,n\in \mathbb{Z}$$

$$tg(\frac{\alpha }{2})=\frac{\sin (\alpha )}{1+\cos (\alpha )},\alpha \ne \pi +2\pi n,n\in \mathbb{Z}$$