Question

Решите cos 165° · cos 285°
Тоже решите sin 75° + sin 15°

Answer 1

1) cos(285*)*cos(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

2)sin75+sin 15 = 2sin (75+15)/2 * cos (75-15)/2 = 2sin 45*cos30

Answer 2

$mathtt{cos165аcos285а=frac{cos(165а-285а)+cos(165а+285а)}{2}=}\mathtt{frac{cos120а+cos450а}{2}=frac{cos(180а-60а)+cos(360а+90а)}{2}=-frac{cos60а}{2}=-frac{1}{4}}$

$mathtt{sin75а+sin15а=sin15а+cos15а=sqrt{2}sin60а=frac{sqrt{6}}{2}=sqrt{1,5}}$