Question

Упростите пожалуйста выражение

Answer 1

$\dfrac{\sin(-\alpha ) \ \text{ctg}(\pi - \alpha )}{\cos(360^{\circ} - \alpha ) \ \text{tg}(2\pi + \alpha )} = \dfrac{-\sin\alpha \ (-\text{ctg} \alpha) }{\cos \alpha \ \text{tg} \alpha } = \dfrac{\sin \alpha \ \text{ctg} \alpha }{\cos \alpha \ \text{tg} \alpha } = \dfrac{\text{tg} \alpha \ \text{ctg} \alpha }{\text{tg} \alpha } = \text{ctg} \alpha$