Question

ctg a-cos2a•ctg a=sin2 a

Answer 1

$Ctg\alpha-Cos2\alpha*Ctg\alpha=Ctg\alpha (1-Cos2\alpha)=\\\\=Ctg\alpha[Sin^{2}\alpha+Cos^{2}\alpha -(Cos^{2}\alpha-Sin^{2}\alpha)]=\\\\=Ctg\alpha(Sin^{2}\alpha +Cos^{2}\alpha-Cos^{2} \alpha+Sin^{2}\alpha)=\frac{Cos\alpha}{Sin\alpha}*2Sin^{2}\alpha=\\\\=2Sin\alpha Cos\alpha=Sin2\alpha\\\\Sin2\alpha =Sin2\alpha$