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当0<x<π2时,函数F(x)=3sin2x+1tAnxCos2x的最...

当π/2

f(x)=(1+2cos²a-1+8sin²x)/(2sinxcosx) =2(cos²x+4sin²x)/(2sinxcosx) =cosx/sinx+4suinx/cosx =cotx+4tanx x是锐角 所以tanx>0.cotx>0 f(x)≥2√(cotx*4tanx)=4 所以最小值=4

(1)∵f(x)=(2cos2x+sin2x)tanx-1∴x≠π2+kπ,k∈Z,∴函数的定义域为:{x|x≠π2+kπ,k∈Z},∵f(x)=(2cos2x+sin2x)tanx-1=2cos2xtanx+sin2xtanx-1=2cosxsinx+2sin2x-1=sin2x-cos2x=2sin(2x-π4)∴f(x)=2sin(2x-π4)∴T=2π2=π,∴函数f(x)的...

解: f(x)=(3sin²x+1)/(tanx·cos²x) =(3sin²x+sin²x+cos²x)/[(sinx/cosx)·cos²x] =(4sin²x+cos²x)/(sinxcosx) =(4tan²x+1)/tanx =4tanx +1/tanx x∈(0,π/2),tanx>0,由均值不等式得: 4tanx+1/ta...

解: (1) tanx有意义,x≠kπ+ π/2,(k∈Z) 函数定义域为{x|x≠kπ+ π/2,k∈Z} f(x)=4tanxsin(π/2 -x)cos(x- π/3) -√3 =4tanxcosxcos(x-π/3)-√3 =4sinx[cosxcos(π/3)+sinxsin(π/3)] -√3 =4sinx[(1/2)cosx+(√3/2)sinx] -√3 =2sinxcosx+2√3sin²x-√...

分子分母同除以 cos^2 x, 得 f(x) = 1/(tanx -tan^2 x) 0= 2√ 1/u(1-u) √ 1/u(1-u) >=2 1/u(1-u) >= 4 f(x) =cos^2x/(cosxsinx-sin^2x) = 1/(tanx -tan^2 x) = 1/u(1-u) >=4 最小值是4

(1)f(x)=2sin(2x?π4)+22cos2x=2(sin2x+cos2x). 由tanx=?13,且x∈(π2,π),可得 sinx=1010,cosx=?31010,∴sin2x=2sinxcosx=-35,cos2x=2cos2x-1=45, 所以:f(x)=25.(2)由(1)得:f(x)=2sin(2x+π4),若x∈[0,π2]时,x+π4∈[π4,5π4]...

f(x)=(1+1/tanx)sin^2x+msin(x+π/4)sin(x-π/4), (1) m=0, f(x)=(1+cosx/sinx)*sin²x =sin²x+sinxcosx =1/2(1-cos2x)+1/2sin2x =1/2sin2x-1/2cos2x+1/2 =√2/2(√2/2sin2x-√2/2cos2x)+1/2 =√2/2sin(2x-π/4)+1/2 ∵x∈(0,π/2) ∴2x-π/4∈(-π...

(1)当m=0时,f(x)=(1+ cosx sinx )sin 2 x=sin 2 x+sinxcosx= 1-cos2x+sin2x 2 = 1 2 [ 2 sin(2x- π 4 )+1]由已知x∈ ( π 8 , 3π 4 ) ,f(x)的值域为(0, 1+ 2 2 )(2)∵ f(x)=(1+ 1 tanx )si n 2 x+msin(x+ π 4 )sin(x- π 4 ) =si...

f(x)=(1+cos2x+8sin^2x)/sin2x =[2(cosx)^2+8(sin)^2x]/2sinxcosx =2(cosx)^2/2sinxcosx+8(sin)^2x/2sinxcosx =cotx+4tanx 00 f(x)>=2根号cotx*4tanx=4 cotx=4tanx是取等号 即(tanx)^2=1/4,tanx=2 所以能取到等号 所以最小值=4

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