41/(sin(-31pi/4)•cos21pi/4)

Решите задачу:

$\sin{\frac{-31\pi}{4}}*\cos{\frac{21\pi}{4}} = \sin{\frac{\pi-32\pi}{4}}*\cos{\frac{\pi + 20\pi}{4}} =\\\\= \sin{(\frac{\pi}{4} - 8\pi)}*\cos{(\frac{\pi}{4} + 5\pi)} =\sin{\frac{\pi}{4}}*\cos{(\frac{\pi}{4} + 4\pi + \pi)} =\\\\= \sin{\frac{\pi}{4}}*\cos{(\frac{\pi}{4} + \pi)} = \sin{\frac{\pi}{4}}*(-\sin{\frac{\pi}{4}}) = -(\frac{1}{\sqrt{2}})^2 = -\frac{1}{2}$

$\frac{41}{\sin{\frac{-31\pi}{4}}*\cos{\frac{21\pi}{4}}} = \frac{41}{-\frac{1}{2}} = -41*2 = \boxed{-82}$