Вычислите (2sin(3π/2+a)-3cos(π+a))/(3sin(π-a)-2cos(π/2-a)), если ctga=4.

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

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

\[= \frac{\cos a}{\sin a} = ctg\ a\]

\[ctg\ a = 4:\]

\[ctg\ a = 4.\]