Вычислите (5sina-6cosa)/(3sina+5cosa), если ctga=-2.

\[\frac{5\sin\alpha - 6\cos\alpha}{3\sin\alpha + 5\cos\alpha} =\]

\[= \frac{5\frac{\sin\alpha}{\sin\alpha} - 6\frac{\cos\alpha}{\sin\alpha}}{3\frac{\sin\alpha}{\sin\alpha} + 5\frac{\cos\alpha}{\sin\alpha}} =\]

\[= \frac{5 - 6ctg\ \alpha}{3 + 5ctg\ \alpha} = \frac{5 - 6 \cdot ( - 2)}{3 + 5 \cdot ( - 2)} =\]

\[= \frac{5 + 12}{3 - 10} = \frac{17}{- 7} = - 2\frac{3}{7}\]