f如何化简f(x)=cos^2x-2sinxcosx-sin^2x,x属于R
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/24 16:06:29
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f如何化简f(x)=cos^2x-2sinxcosx-sin^2x,x属于R
f如何化简f(x)=cos^2x-2sinxcosx-sin^2x,x属于R
f如何化简f(x)=cos^2x-2sinxcosx-sin^2x,x属于R
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。