Question

Упростить :
(cos15°-cos75°)-(sin75°+sin15°)

Answer 1

$15=45-30; ; 75 = 45+30;\ (cos15-cos75)-(sin75+sin15)\cos(45-30)-cos(45+30)-sin(45+30)+sin(45-30)=\cos45cos30+sin45sin30-cos45cos30+sin45sin30-\-sin45cos30-cos45sin30+sin45cos30-cos45sin30=\=2sin45sin30+2sin45cos30=2*frac{sqrt2}{2}*frac{1}{2}+2*frac{sqrt2}{2}*frac{sqrt3}{2}=frac{sqrt2+sqrt6}{2}$