已知sin(x-3π/4)cos(x-π/4)=- - 知识问答

已知sin(x-3π/4)cos(x-π/4)=-1/4,则cosx等于

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sin(x-3π/4)
=sin[π-(π/4-x)]
=sin(π/4-x)
=-sin(x-π/4)
sin(x-3π/4)cos(x-π/4)
=-sin(x-π/4)cos(x-π/4)
=-sin(2x-π/2)/2=-1/4
cos(2x)=1/2
2x=60°
x=30°
cosx=cos30等于根号3/2

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