Sin a Sin a ____ + _____ 1+cos a 1-cos a

Решите задачу:

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