Вычислите (2sin(3π/2-a)-3cos(π-a))/(3sin(π+a)-2cos(3π/2+a)), если ctga=5.

\[\frac{2\sin\left( \frac{3\pi}{2} - a \right) - 3\cos(\pi - a)}{3\sin(\pi + a) - 2\cos\left( \frac{3\pi}{2} + a \right)} =\]

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

\[= \frac{\cos a}{- 5\sin a} = - \frac{\text{ctg\ a}}{5}\]

\[ctg\ a = 5:\]

\[- \frac{\text{ctg\ a}}{5} = - \frac{5}{5} = - 1.\]