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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

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...

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

f(x)=(1+tanx)?cos2xcos2x+sin2x=12+122sin(2x+π4)因为定义域为(0,π4),所以sin(2x+π4)∈(22,1],所以f(x)的值域为[2+24,1).故答案为:[2+24,1).

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-√...

为什么sin2X=2tanX/(1+tan²X) 证明:sin2x=2sinxcosx 【cos²x+sin²x=1,在分母上写上cos²x+sin²x就是写个1,分式的值不变】 =2sinxcosx/(cos²x+sin²x) 【分子分母同除以cos²x,便得:】 =2tanx/(1+tan&...

f(x)=(cos²x+sinxcosx)/(sin2x+cos2x) =(1/2+1/2cos2x+1/2sin2x)/(sin2x+cos2x) =(1/2)+(1/2)/(sin2x+cos2x) =(1/2)+1/[2√2sin(2x+π/4)] 0

(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+2 cosx^2 -1+8sinx^2) /2sinxcosx =(cosx^2+4sinx^2) /sinxcosx 同时除以cosx^2 =(1+4tanx^2)/tanx =1/tanx+4tanx ∵0<x<π ∴1/tanx,4tanx∈R+ ∴原式=1/tanx+4tanx≥2根号下1/tanx•4tanx=4 当且仅当1/tanx=4tanx时,即tanx=½...

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