已知:sin(x-3p/4)cos(x-p/4)=-1/4,则cos4x的等于____.

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/13 03:53:50
已知:sin(x-3p/4)cos(x-p/4)=-1/4,则cos4x的等于____.
x){}KUQk\o_ dX&:O;fL*jyɮx гI*ҧD~ օ. dFBRbVDRj F3B/!Q v0؋`./&@%~LT$j0J&SmkjM-^M$Q=S<;P|h

已知:sin(x-3p/4)cos(x-p/4)=-1/4,则cos4x的等于____.
已知:sin(x-3p/4)cos(x-p/4)=-1/4,则cos4x的等于____.

已知:sin(x-3p/4)cos(x-p/4)=-1/4,则cos4x的等于____.
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