Соотношения:

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

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

$$1+ctg\,^2\alpha=\frac{1}{\sin^2\alpha},$$

$$tg \,\alpha \cdot ctg \,\alpha = 1.$$

Формулы сложения:

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

$$\sin(\alpha-\beta) = \sin\alpha \cos\beta - \cos\alpha \sin\beta,$$

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

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

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

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

$$ctg \,(\alpha+\beta) = \frac{ctg \,\alpha \cdot ctg \,\beta - 1}{ctg \,\beta + ctg \,\alpha},$$

$$ctg \,(\alpha-\beta) = \frac{ctg \,\alpha \cdot ctg \,\beta + 1}{ctg \,\beta - ctg \,\alpha}.$$

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