Question

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

Answer 1

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