Вычислите (5sina-3cosa)/(3sina+2cosa), если tga=-2.

\[\frac{5\sin\alpha - 3\cos\alpha}{3\sin\alpha + 2\cos\alpha} =\]

\[= \frac{5\frac{\sin\alpha}{\cos\alpha} - 3\frac{\cos\alpha}{\cos\alpha}}{3\frac{\sin\alpha}{\cos\alpha} + 2\frac{\cos\alpha}{\cos\alpha}} =\]

\[= \frac{5tg\ \alpha - 3}{3tg\ \alpha + 2} = \frac{5 \cdot ( - 2) - 3}{3 \cdot ( - 2) + 2} =\]

\[= \frac{- 10 - 3}{- 6 + 2} = \frac{- 13}{- 4} = \frac{13}{4} = 3\frac{1}{4}\]