Question

Хелп плиз (23б) .Примеры на фото

Answer 1

$sin frac{7pi }{18} cdot sinfrac{5pi }{18}cdot sinfrac{pi }{18}=[, frac{pi }{18}=10^circ , ]= sin70^circ cdot sin50^circ cdot sin10^circ = \\= frac{1}{2}cdot sin10^circ cdot (2sin70^circ cdot sin50^circ )=\\=frac{1}{2} sin10^circ (cos(70^circ -50^circ)-cos(70^circ +50^circ ))=\\= frac{1}{2}sin10^circ cdot (cos20^circ -cos120^circ )=[, cos2 alpha =1-2sin^2 alpha ]=\\=frac{1}{2}sin10^circ cdot (underbrace {1-2sin^210^circ }_{cos20^circ }-underbrace {cos(90^circ +30)}_{-sin30^circ })=[, sin30^circ =frac{1}{2}, ]=$

$= frac{1}{2}sin10^circ cdot (1-2sin^210^circ +frac{1}{2})=frac{1}{2}sin10^circ cdot ( frac{3}{2}-2sin^210^circ )=\\=frac{1}{2}sin10^circcdot frac{3-4sin^210^circ }{2}= frac{1}{4}cdot (3sin10^circ -4sin^310^circ )=\\=[, sin3varphi =3sinvarphi -4sin^3varphi , ]= frac{1}{4}cdot sin(3cdot 10^circ )=frac{1}{4}cdot sin 30^circ =\\= frac{1}{4}cdot frac{1}{2}=frac{1}{8}$