Question

Найдите значение выражения

Answer 1

$cosfrac{5pi }{12}=cos(frac{6pi -pi }{12})=cos(frac{pi}{2}-frac{pi}{12})=sinfrac{pi}{12}\\8sqrt3cosfrac{5pi }{12}cosfrac{pi}{12}sinfrac{pi}{6}=8sqrt3(sinfrac{pi}{12}cosfrac{pi}{12})sinfrac{pi}{6}=8sqrt3(frac{1}{2}sinfrac{pi}{6})sinfrac{pi}{6}=\\=4sqrt3cdot (frac{1}{2})^2=sqrt3$