已知sin (x-3pai /4)cos (x-pai /4)=-1/4,则cos 4x 的值等于

1个回答

  • 用p代表π

    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

    你的好评是我前进的动力.

    我在沙漠中喝着可口可乐,唱着卡拉ok,骑着狮子赶着蚂蚁,手中拿着键盘为你答题!