Вычислите: [latex] \frac{5sin ( \frac{5 \pi }{2}- \alpha )}{8sin( \pi - \alpha )} \alpha = \frac{5 \pi }{4} [/latex]

[latex] \frac{5sin( \frac{5 \pi }{2} - \alpha) }{8sin( \pi - \alpha )} = \frac{5sin(2 \pi + \frac{ \pi }{2}- \alpha )}{8sin \alpha } = \frac{5sin( \frac{ \pi }{2}- \alpha ) }{8sin \alpha } = \frac{5cos \alpha }{8sin \alpha } = \frac{5}{8} *ctg \alpha [/latex][latex] \frac{5}{8} *ctg \alpha =\frac{5}{8}*1= \frac{5}{8} =0,625 [/latex]