Question

Упростите выражение

Answer 1

$( \frac{Sin \alpha +Ctg \alpha }{1+Sin \alpha *tg \alpha }) ^{2}-Ctg \alpha =( \frac{Sin \alpha + \frac{Cos \alpha }{Sin \alpha } }{1+Sin \alpha * \frac{Sin \alpha }{Cos \alpha } }) ^{2}-Ctg \alpha =[ \frac{(Sin ^{2} \alpha +Cos \alpha )*Cos \alpha \alpha }{Sin \alpha *(Cos \alpha +Sin ^{2} \alpha )}] ^{2}-Ctg ^{2} \alpha =Ctg ^{2} \alpha -Ctg ^{2} \alpha =0$