Монгол Бодлогын Сан

Заавар: $$\tg2\alpha=\dfrac{2\tg\alpha}{1-\tg^2\alpha}$$

Бодолт: $\tg2\alpha=\dfrac{2\cdot 3}{1-3^2}=-\dfrac34$

$$\begin{align*} \dfrac{2\sin2\alpha-3\cos2\alpha}{4\sin2\alpha+5\cos2\alpha}&=\dfrac{2\cdot\dfrac{\sin2\alpha}{\cos2\alpha}-3\cdot\dfrac{\cos2\alpha}{\cos2\alpha}}{4\cdot\dfrac{\sin2\alpha}{\cos2\alpha}+5\cdot\dfrac{\cos2\alpha}{\cos2\alpha}}=\\ &=\dfrac{2\tg2\alpha-3}{4\tg2\alpha+5}=\dfrac{-\frac32-3}{-3+5}=-\dfrac{9}{4} \end{align*}$$