Question

Сократить. Картинка прилагается.

Answer 1

$\displaystyle \left(\frac{\cos^3\alpha}{\sin\alpha}-\frac{\sin^3\alpha}{\cos\alpha}\right)\cdot {\rm tg}\,2\alpha=\left(\frac{\cos^4\alpha-\sin^4\alpha}{\sin\alpha\cos\alpha}\right)\cdot \frac{\sin2\alpha}{\cos2\alpha}=\\ \\ \\ =\frac{2\left(\cos^2\alpha-\sin^2\alpha\right)\left(\cos^2\alpha+\sin^2\alpha\right)}{2\sin\alpha\cos\alpha}\cdot\frac{\sin2\alpha}{\cos2\alpha}=\frac{2\cos2\alpha\cdot 1}{\sin2\alpha}\cdot\frac{\sin2\alpha}{\cos2\alpha}=2$