已知：sin(x-3p/4)cos(x-p/4)=-1/4,则cos4x的等于____. 怎么做的？？？
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sin(x-3p/4)cos(x-p/4)=-1/4
sin(x-3p/4)sin[p/2-(x-p/4)]=-1/4
sin(x-3p/4)sin(3p/4-x)=-1/4
sin(3p/4-x)sin(x-3p/4)=1/4
[sin(3p/4-x)]^2=1/4
[sin(p-p/4-x)]^2=1/4
[sin(x+p/4)]^2=1/4
cos4x
=-cos(4x+p)
=-cos[4*(x+p/4)]
=-2cos[2*(x+p/4)]^2+1
=-2{1-2[sin(x+p/4)]^2}^2+1
=-2{1-2(1/4)}^2+1
=0.5
sin(x-3p/4)sin[p/2-(x-p/4)]=-1/4
sin(x-3p/4)sin(3p/4-x)=-1/4
sin(3p/4-x)sin(x-3p/4)=1/4
[sin(3p/4-x)]^2=1/4
[sin(p-p/4-x)]^2=1/4
[sin(x+p/4)]^2=1/4
cos4x
=-cos(4x+p)
=-cos[4*(x+p/4)]
=-2cos[2*(x+p/4)]^2+1
=-2{1-2[sin(x+p/4)]^2}^2+1
=-2{1-2(1/4)}^2+1
=0.5
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