Question

Решите подробно пример на фото.

Answer 1

$\dfrac{\sin \alpha }{1-\cos \alpha } -\ \dfrac{\sin \alpha }{\cos \alpha +1} = \dfrac{\sin \alpha \cdot(\cos \alpha +1)-\sin \alpha (1-\cos \alpha )}{(1-\cos \alpha )(1+\cos \alpha )} =\\\\\\= \dfrac{\sin \alpha \cos \alpha +\sin \alpha -\sin \alpha +\sin \alpha \cos \alpha }{1-\cos^2 \alpha } = \dfrac{2\sin \alpha \cos \alpha }{\sin^2 \alpha } = \dfrac{2\cos \alpha }{\sin \alpha } =\\\\\\=2\tan \alpha$