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