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

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

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

\[= 5ctg\ a = \frac{5}{\text{tg\ a}}\]

\[tg\ a = 5:\]

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