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Решите задачу:

$Sin2\alpha +Cos2\alpha *Ctg\alpha =2Sin\alpha Cos\alpha +(Cos^{2}\alpha -Sin^{2}\alpha )*\frac{Cos\alpha}{Sin\alpha}=2Sin\alpha Cos\alpha +\frac{Cos^{3}\alpha}{Sin\alpha}-\frac{Sin^{2}\alpha*Cos\alpha}{Sin\alpha} =2Sin\alpha Cos\alpha+\frac{Cos^{3}\alpha}{Sin\alpha} -Sin\alpha Cos\alpha=Sin\alpha Cos\alpha +\frac{Cos^{3}\alpha}{Sin\alpha}=\frac{Sin^{2}\alpha Cos\alpha+Cos^{3}\alpha}{Sin\alpha}=\frac{Cos\alpha(Sin^{2}\alpha+Cos^{2}\alpha)}{Sin\alpha}=\frac{Cos\alpha}{Sin\alpha}=Ctg\alpha$

$Ctg2\alpha -tg2\alpha =\frac{1}{tg2\alpha} -tg2\alpha =\frac{1-tg^{2}2\alpha}{tg2\alpha} =\frac{1}{\frac{1}{2}tg4\alpha} =\frac{2}{tg4\alpha}$