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

$$tg\alpha=\frac{sin\alpha}{cos\alpha}; (cos\alpha \neq 0);$$

$$ctg\alpha=\frac{cos\alpha}{sin\alpha}; (sin\alpha \neq 0);$$

$$tg\alpha \cdot ctg\alpha=1; (sin\alpha \cdot cos\alpha \neq 0);$$

$$ctg^2\alpha+1=\frac{1}{sin^2\alpha}; (sin\alpha \neq 0);$$

$$tg^2\alpha+1=\frac{1}{cos^2\alpha}; (cos\alpha \neq 0).$$

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

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

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

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

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

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