化简cos20°-cos40°-cos80°等于?

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化简cos20°-cos40°-cos80°等于?
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化简cos20°-cos40°-cos80°等于?
化简cos20°-cos40°-cos80°等于?

化简cos20°-cos40°-cos80°等于?
cos20°-cos40°-cos80°
=cos20°-(cos40°+cos80°)
=cos20°-2cos60°*cos20°
(这一步运用了和差化积的公式,即:
cos α+cos β=2cos[(α+β)/2]·cos[(α-β)/2],
此处可认为α=80°,β=40°)
=cos20°-cos20°
=0