Question

Тождество,,,..,,..,.,.,.,.,.,.,.,.,.,..,.,.,.,.,..,.,.,.,.,.,..,.,.,.,..,.,.,.

Answer 1

$\displaystyle \frac{2\sin^2\alpha}{{\rm tg}2\alpha\cdot {\rm tg}\alpha}=\frac{2\sin^2\alpha\cos2\alpha\cos\alpha}{\sin2\alpha\sin\alpha}=\frac{\sin2\alpha\sin\alpha\cos 2\alpha}{\sin2\alpha\sin\alpha}=\\ \\ \\ =\cos 2\alpha=\cos^2\alpha-\sin^2\alpha$