Question

Упростить выражение

Answer 1

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