Question

Решите!!!
соs(10) sin (80) + sin^2 (280) соs^2 (100) + sin^2 (170) sin^2 (350) =

Answer 1

$cos10cdot sin80+sin^2280cdot cos^2100+sin^2170cdot sin^2350=\\=cos10cdot sin(90-10)+sin^2(270+10)cdot cos^2(90-10)+\\+sin^2(180-10)cdot sin^2(360-10)=\\=cos10cdot cos10+cos^210cdot sin^210+sin^210cdot sin^210=\\=cos^210+sin^210(cos^210+sin^210)=\\=cos^210+sin^210cdot 1=cos^210+sin^210=1$