Сократить (sin alfa/ 1+ cos alfa ) + (1+cos akfa/sin alfa)

Решите задачу:

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