Question

Решите, пожалуйста:

cos 8° cos 37° - cos82° cos53°

Answer 1

cos 8° cos 37° - cos82° cos53°=
(cos(8°+37°)+cos(8°-37°))/2- (cos(82°+53°)+cos(82°-53°))/2=
(cos45°+cos29°)/2-(cos135°+cos29°)/2=cos45°/2-cos(90°+45°)=cos45°/2-sin45°/2=√2/4-√2/4=0