Question

найти значение выражения sin20*sin50*sin70/sin80

Answer 1

$frac{sin20*sin50*sin70}{sin80} = frac{(2cos20*sin20)*sin50*sin70}{2cos20*sin80} = frac{sin40*sin(90-40)*sin70}{2cos20*sin80} =\\= frac{sin40*cos40*sin70}{2cos20*sin80} = frac{frac{1}{2}sin80*sin70}{2cos20*sin80} =frac{sin(90-20)}{4cos20}=frac{cos20}{4cos20}=frac{1}{4}\\P.S.; ; ; sin(90- alpha )=cos alpha ; ; ;; ; ; cos(90- alpha )=sin alpha$