Question

sin^2 a (1- ctg^2a)=

Answer 1

$Sin^{2}\alpha*(1-Ctg^{2}\alpha)=Sin^{2}\alpha*(1-\frac{Cos^{2}\alpha}{Sin^{2}\alpha})=Sin^{2}\alpha*\frac{Sin^{2}\alpha-Cos^{2}\alpha}{Sin^{2}\alpha} =\\\\=Sin^{2}\alpha-Cos^{2}\alpha =-\underbrace{(Cos^{2}\alpha-Sin^{2}\alpha)}_{Cos2\alpha}=\boxed{-Cos2\alpha }$