字典翻译 问答 小学 数学 (cos80°-cos20°)/sin80°+sin20°)=顺便再回答个cos20°+cos100°+cos140°=
问题标题:
(cos80°-cos20°)/sin80°+sin20°)=顺便再回答个cos20°+cos100°+cos140°=
问题描述:

(cos80°-cos20°)/sin80°+sin20°)=

顺便再回答个

cos20°+cos100°+cos140°=

安维廉回答:
  (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
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