Вычислите (4sina-7cosa)/(5sina+3cosa), если ctga=-3.

\[\frac{4\sin\alpha - 7\cos\alpha}{5\sin\alpha + 3\cos\alpha} =\]

\[= \frac{4\frac{\sin\alpha}{\sin\alpha} - 7\frac{\cos\alpha}{\sin\alpha}}{5\frac{\sin\alpha}{\sin\alpha} + 3\frac{\cos\alpha}{\sin\alpha}} =\]

\[= \frac{4 - 7ctg\ \alpha}{5 + 3ctg\ \alpha} = \frac{4 - 7 \cdot ( - 3)}{5 + 3 \cdot ( - 3)} =\]

\[= \frac{4 + 21}{5 - 9} = \frac{25}{- 4} = - 6\frac{1}{4}\]