已知sin(x-3/4π)cos(X-π/4)=-1/4,求cos4x的值.要过程

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已知sin(x-3/4π)cos(X-π/4)=-1/4,求cos4x的值.要过程已知sin(x-3/4π)cos(X-π/4)=-1/4,求cos4x的值.要过程已知sin(x-3/4π)cos(X

已知sin(x-3/4π)cos(X-π/4)=-1/4,求cos4x的值.要过程
已知sin(x-3/4π)cos(X-π/4)=-1/4,求cos4x的值.要过程

已知sin(x-3/4π)cos(X-π/4)=-1/4,求cos4x的值.要过程
sin(x-3/4π)=sin(x+π/4-π)=-sin(x+π/4)
也就是sin(x+π/4)cos(X-π/4)=1/4
sin(x+π/4)cos(X-π/4)=sin(x+π/4+x-π/4)+sin(x+π/4-x+π/4)=sin2xsinπ/2=sin2x=1/4
cos4x=1-2sin^2 2x=1-1/16=15/16

sin(x-3/4π)cos(x-π/4)
=-sin(x+π/4) cos(x-π/4)
(诱导公式π+α)
=-cos^2(x-π/4))
(诱导公式π/2-α)
=-(1+cos(2x+π/2))/2
(倍角余弦)
=-1/2+sin2x=-1/4
(诱导公式π/2+α)
sin2x=1/4.
cos4x=1-cos^22x
=15/16.