Формулы произведения тригонометрических функций

$$sin\alpha \cdot sin\beta = \frac{cos(\alpha - \beta)-cos(\alpha + \beta)}{2}$$

$$sin\alpha \cdot cos\beta = \frac{sin(\alpha - \beta)+sin(\alpha + \beta)}{2}$$

$$cos\alpha \cdot cos\beta = \frac{cos(\alpha - \beta)+cos(\alpha + \beta)}{2}$$

\begin{align} tg\alpha \cdot tg\beta & = \frac{cos(\alpha - \beta)-cos(\alpha + \beta)}{cos(\alpha - \beta)+cos(\alpha + \beta)}\\ &= \frac{tg\alpha + tg\beta}{ctg\alpha + ctg\beta} \end{align}

\begin{align} ctg\alpha \cdot ctg\beta & = \frac{cos(\alpha - \beta)+cos(\alpha + \beta)}{cos(\alpha - \beta)-cos(\alpha + \beta)}\\ &= \frac{ctg\alpha + ctg\beta}{tg\alpha + tg\beta} \end{align}

$$tg\alpha \cdot ctg\beta = \frac{sin(\alpha - \beta)+sin(\alpha + \beta)}{sin(\alpha + \beta)-sin(\alpha - \beta)}$$