Question

41/(sin(-31pi/4)•cos21pi/4)

Answer 1

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

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