Question

Упростить (tga-sina)*(cos^2a/sina +ctga)

Answer 1

$(tg\alpha-Sin\alpha)*(\frac{Cos^{2}\alpha}{Sin\alpha}+Ctg\alpha)=(\frac{Sin\alpha }{Cos\alpha}-Sin\alpha)*(\frac{Cos^{2}\alpha}{Sin\alpha}+\frac{Cos\alpha}{Sin\alpha })=\\\\=\frac{Sin\alpha-Sin\alpha*Cos\alpha}{Cos\alpha}*\frac{Cos^{2}\alpha+Cos\alpha}{Sin\alpha}=\frac{Sin\alpha(1-Cos\alpha)*Cos\alpha(Cos\alpha+1)}{Cos\alpha*Sin\alpha}=\\\\=(1-Cos\alpha)(1+Cos\alpha)=1-Cos^{2}\alpha=Sin^{2}\alpha \\\\Otvet:\boxed{Sin^{2}\alpha}$