докажите тождество 2/cosa- cosa/1+sina=1+sina/cosa

Решите задачу:

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