Question

Cos165*×cos285* помогитеее плзз

Answer 1

Cos(a+b) = cos(a)*cos(b) - sin(a)*sin(b);
cos(a-b) = cos(a)*cos(b) + sin(a)*sin(b);
складываем последние два уравнения,
cos(a+b) + cos(a-b) = 2*cos(a)*cos(b);
cos(a)*cos(b) = (1/2)*( cos(a+b) + cos(a-b) );
cos(285*)*co(165*) = (1/2)*( cos(285*+165*) + cos(285*-165*) ) =
= (1/2)*( cos(450*) + cos(120*) ) = (1/2)*( cos(360*+90*) + cos(180*-60*) ) = (1/2)*(cos(90*) - cos(60*) ) = (1/2)*( 0 - (1/2)) = -1/4 = -0,25.