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Решите задачу:

$\frac{8}{sin(- \frac{27\pi}{4} )cos( \frac{31\pi}{4} )} = \frac{8}{-sin( \frac{27\pi}{4} )cos( \frac{31\pi}{4} )} = \frac{8}{-sin( \frac{12*2\pi+3\pi}{4} )cos( \frac{12*2\pi+7\pi}{4} )} =$
$=- \frac{8}{sin(3*2\pi+ \frac{3\pi}{4} )cos( 3*2\pi+\frac{7\pi}{4} )} =- \frac{8}{sin(\frac{3\pi}{4} )cos( \frac{7\pi}{4} )}$
$=- \frac{8}{sin(\frac{3\pi}{4} )cos( \pi+\frac{3\pi}{4} )} =- \frac{8}{sin(\frac{3\pi}{4} )*(-cos( \frac{3\pi}{4} ))} =\frac{8}{sin(\frac{3\pi}{4} )*cos( \frac{3\pi}{4} )} =$
$=\frac{16}{2sin(\frac{3\pi}{4} )*cos( \frac{3\pi}{4} )} = \frac{16}{sin \frac{3\pi}{2}}= \frac{16}{-1}=-16$