题目

(cos80°-cos20°)/sin80°+sin20°)=
顺便再回答个
cos20°+cos100°+cos140°=

提问时间：2020-12-28

答案

(cos80°-cos20°)/(sin80°+sin20°)
=[cos(50°+30°)-cos(50°-30°)]/[sin(50°+30°)+sin(50°-30°)]
=[(cos50°cos30°-sin50°sin30°)- (cos50°cos30°+sin50°sin30°)]/[ (sin50°cos30°+cos50°sin30°)+ (sin50°cos30°-cos50°sin30°)]
=(-2sin50°sin30°)/ (2sin50°cos30°)
= -2sin30°/ cos30°
= -tan30°
= -√3/3
cos20°+cos100°+cos140°
= cos (80°-60°)+cos100°+cos(80°+60°)
= (cos80°cos60°+sin80°sin60°)+cos100°+ (cos80°cos60°-sin80°sin60°)
= 2cos80°cos60°+cos100°
= cos80°+cos100°
= cos80°-cos80°
=0