cos20°-cos40°-cos80°=

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cos20°-cos40°-cos80°
=cos20°-cos（60°-20°）-cos（60°+20°）
=cos20°-（cos60°cos20°+sin60°sin20°）-（cos60°cos20°-sin60°sin20°）
=cos20°-cos60°cos20°-sin60°sin20°-cos60°cos20°+sin60°sin20°
=cos20°-2cos60°cos20°
=cos20°-cos20°
=0．故答案为：0
======以下答案可供参考======
供参考答案1:
0供参考答案2:
cos20-(cos40+cos80)
=cos20-[cos(60-20)+cos(60+20)]
=cos20-[(cos60c0s20+sin60sin20)+(cos60cos20-sin60sin20)]
=cos20-2cos60cos20
=cos20-2*1/2*cos20
=cos20-cos20
=0