Question

Выражение: sin^2a+ sin(p-a)*cos(p/2-a)/tg(p+a)*ctg(3p/2a) , a ≠ pn/2 , n ∈ z

Answer 1

$\frac{Sin ^{2} \alpha +Sin( \pi - \alpha )*Cos( \frac{ \pi }{2}- \alpha ) }{tg( \pi + \alpha )*Ctg( \frac{3 \pi }{2}- \alpha ) } = \frac{Sin ^{2} \alpha +Sin \alpha *Sin \alpha }{tg \alpha *(tg \alpha )} = \frac{Sin ^{2} \alpha +Sin ^{2} \alpha }{tg ^{2} \alpha }= \frac{2Sin ^{2} \alpha }{ \frac{Sin ^{2} \alpha }{Cos ^{2} \alpha } } =$$=2Cos ^{2} \alpha$