sin(x+y)sin(x-y)=k,求cos^2x-cos^2y

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sin(x+y)sin(x-y)=k,求cos^2x-cos^2y
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sin(x+y)sin(x-y)=k,求cos^2x-cos^2y
sin(x+y)sin(x-y)=k,求cos^2x-cos^2y

sin(x+y)sin(x-y)=k,求cos^2x-cos^2y
-2k=cos2x-cos2y
=[2(cosx)^2-1]-[2(cosy)^2-1]
=2[(cosx)^2-(cosy)^2]
cos^2x-cos^2y=-k

这道题其实就是利用积化和差公式,有 sinαsinβ=-1/2[cos(α+β)-cos(α-β)]
那么利用公式,答案就是 -2k