f如何化简f（x）=cos^2x-2sinxcosx-sin^2x,x属于R

来源：学生作业学帮网编辑：学帮网时间：2024/06/07 00:06:17

f（x）=cos^2x-sin^2x-2sinxcosx
=cos2x-sin2x

f（x）=cos^2x-2sinxcosx-sin^2x=1-sin^2x-2sinxcosx-sin^2x=
1-2sin^2x-2sinxcosx=1-2sin^2x-sin2x=-(sin2x+1)(2sinx+1)

f（x）=cos^2x-sin^2x-2sinxcosx
=cos2x-sin2x
=(cos(2x+Pi/4))*2^0.5
其中：2^0.5为根号2，Pi为圆周率。