−4cos(5 × π / 12) / sin(π / 12) Найдите значение выражения.

[latex] \frac{-4cos( \frac{5 \pi }{12}) }{sin \frac{ \pi }{12} } = \frac{-4cos75}{sin15}= \frac{-4cos(30+45)}{ \frac{ \sqrt{6}- \sqrt{2} }{4} }= \frac{-4(cos30cos45-sin30sin45)}{ \frac{ \sqrt{6}- \sqrt{2} }{4} } } =[latex] \frac{-4( \frac{ \sqrt{6}- \sqrt{2} }{4}) }{ \frac{ \sqrt{6}- \sqrt{2} }{4} }=-4 [/latex]