化简函数f（x）=[(1+cos2x)²-2cos2x-1]/[sin(π/4+x）*sin(π/4-x)]

来源：学生作业帮编辑：神马作文网作业帮分类：数学作业时间：2024/11/11 12:39:25

(1+cos2x)²-2cos2x-1
=1+2cos(2x)+cos²(2x)-2cos(2x)-1
=cos²(2x)
=[cos²(x)-sin²(x)]²
=[cos(x)-sin(x)]² * [cos(x)+sin(x)]²

sin(π/4+x)=sin(π/4)cos(x)+cos(π/4)sin(x)=[cos(x)+sin(x)]/√2
sin(π/4-x)=sin(π/4)cos(x)-cos(π/4)sin(x)=[cos(x)-sin(x)]/√2

f(x)=[cos(x)-sin(x)]² * [cos(x)+sin(x)]² * [cos(x)-sin(x)] / [cos(x)+sin(x)]
= [cos(x)-sin(x)]³ * [cos(x)+sin(x)]
= [cos(x)-sin(x)]² * [cos²(x)-sin²(x)]
=[cos²(x)-2sin(x)cos(x)+sin²(x)] * cos(2x)
=[1-sin(2x)]cos(2x)

化简函数f（x）=[(1+cos2x)²-2cos2x-1]/[sin(π/4+x）*sin(π/4-x)] 已知函数f（x）=2sin²（π/4+x）-根号3cos2x f(x)=((1+cos2x)^2-2cos2x-1)/(sin(π/4+x)sin(π/4-x)) 已知函数f(x)=cos2x/[sin(π/4-x)] 已知函数f（x）=sin（π-x）sin（π2-x）+cos2x 已知函数f(x)=2sin^2（π/4+x）-根号3cos2x 已知函数f(x)=2sin的平方(x+π\4)-根号3cos2x-1 已知函数f(x)=（4cos^4x-2cos2x-1）/[sin(π/4+x)·sin^2(π/4-x)]化简已知函数f(x)=（4cos^4x-2cos2x-1）/[sin(π/4+x)·sin(π/4-x)]化简已知函数f(x)=2sin²(π/4+x)-（√2）cos2x-1,x∈R 1.求f(x)最小值已知函数f(x)=2sin^2(π\4+x)-根号3cos2x-1,x∈R 0＜X＜π/4,求函数f(x)=(cos2x+1)/(sinxcosx-sin^2x)的最小值!