Question

Помогите решить пример

Answer 1

$\frac{2Sin\alpha Cos\beta+Sin(\beta-\alpha)}{Cos(\alpha-\beta)-2Sin\alpha Sin\beta}=\frac{2Sin\alpha Cos\beta-Sin(\alpha-\beta)}{Cos(\alpha-\beta)-2Sin\alpha Sin\beta}=\frac{2Sin\alpha Cos\beta-Sin\alpha Cos\beta+Cos\alpha Sin\beta}{Cos\alpha Cos\beta+Sin\alpha Sin\beta-2Sin\alpha Sin\beta}=\\\\=\frac{Sin\alpha Cos\beta+Cos\alpha Sin\beta}{Cos\alpha Cos\beta-Sin\alpha Sin\beta}= \frac{Sin(\alpha+\beta)}{Cos(\alpha+\beta)}=\boxed{tg(\alpha+\beta)}$