∵cos2α-cos2β=m,
∴sin(α+β)sin(α-β)=(sinαcosβ)2-(cosαsinβ)2
=sin2αcos2β-cos2α(1-cos2β)=sin2αcos2β-cos2α+cos2αcos2β
=(sin2αcos2β+cos2αcos2β)-cos2α=cos2β-cos2α=-m,
故答案为:-m.
已知cos2α-cos2β=m,那么sin(α+β)sin(α-β)=_.
已知cos2α-cos2β=m,那么sin(α+β)sin(α-β)=______.
数学人气:999 ℃时间:2020-04-13 18:34:27
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