已知函数f(x)=[2cos^4x-2cos^x+1/2]/[tan(π/4-x)sin^2(π/4+x)],求f(x)
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/23 12:03:33
已知函数f(x)=[2cos^4x-2cos^x+1/2]/[tan(π/4-x)sin^2(π/4+x)],求f(x)的值域
tan(π/4-x)= (tanπ/4-tanx)/(1+tanπ/4tanx) = (1-tanx)(1+tanx) = (cosx-sinx)/(cosx+sinx)
sin^2(π/4+x) = (√2/2sinx+√2/2cosx)^2= 1/2(sinx+cosx)^2
f(x) = [2cos^4x-2cos^2x+1/2]/[tan(π/4-x)sin^2(π/4+x)]
=[2cos^4x-2cos^2x+1/2]/[ (cosx-sinx)/(cosx+sinx)*1/2(sin+cosx)^2]
=[4cos^4x-4cos^2x+1]/[ (cosx-sinx)(cosx+sinx)]
= (2cos^2x-1)^2 / (cos^2x-sin^2x)
=[cos(2x)]^2 / cos(2x)
= cos(2x) ∈【-1,1】
值域:【-1,1】
sin^2(π/4+x) = (√2/2sinx+√2/2cosx)^2= 1/2(sinx+cosx)^2
f(x) = [2cos^4x-2cos^2x+1/2]/[tan(π/4-x)sin^2(π/4+x)]
=[2cos^4x-2cos^2x+1/2]/[ (cosx-sinx)/(cosx+sinx)*1/2(sin+cosx)^2]
=[4cos^4x-4cos^2x+1]/[ (cosx-sinx)(cosx+sinx)]
= (2cos^2x-1)^2 / (cos^2x-sin^2x)
=[cos(2x)]^2 / cos(2x)
= cos(2x) ∈【-1,1】
值域:【-1,1】
三角函数已知f(x)=(2cos^4x—2cos²x+1/2)/(2tan(π/4—x)sin²(x
已知函数f(x)=4cos²x+sin²x-4cosx-2 (1)求f(π/3)的值.(2)求f(x
已知f(x)=cos^2x/1+sin^2x求f'(π/4)
已知函数f(x)=sin²(π/4+x)+cos²x+1/2求最值
已知函数f(x)=cos^4x-2sinxcosx-sin^4x
已知函数f(x)=cos^4(x)+(2根号3)sinxcosx-sin^4(x)
已知函数f(x)=cos 4 x-2sinxcosx-sin 4 x
已知函数f(x)=(1/2)cos^x+((根号3)/2)sin x cos x -(1/4),x属于R,求函数f(x)
已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)=sin(2x-π/6) ,
已知函数f(x )=sin ^2x +2√3sin x cos x +3cos^x 、求函数f (x )的单调增区间
已知函数f(x)=2cos^2 x+2sinxcosx-1 化简后f(x)=√2sin(2x+π/4) 求f(x)在[0
已知函数f(x)=(1+1/tanx)sin(x)^2 -2sin(x+π/4)*cos(x+π/4)