Question

$\frac{sin \alpha }{1 - \cos \alpha } - ctg \alpha$
Помогите решить

Answer 1

$\frac{sin \alpha }{1 - \cos \alpha } - ctg \alpha = \frac{sin \alpha }{1 - \cos \alpha } - \frac{cos\alpha}{sin\alpha}= \frac{sin^2 \alpha -cos\alpha(1-cos\alpha)}{(1-cos\alpha)sin\alpha}=\\ \frac{sin^2 \alpha -cos\alpha+cos^2\alpha}{(1-cos\alpha)sin\alpha}= \frac{1-cos\alpha}{(1-cos\alpha)sin\alpha}=\frac{1}{sin\alpha}$