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当0<x<π/4时,函数F(x)=Cos^2x/Cosxsinx%sin^2x的...

f(x)=cos^2x/(cosxsinx-sin^2x) =1/(tgx-tg^2x) =1/[-(tgx-1/2)+1/4] 0

函数化简=2cos2x/sin2x-sin2x.即:f(x)=2cosX/sinX-sinX,X∈(0,π/2)的最小值。求导为-2/(sinX)^2-cosX,此小于0,减函数。则:x=π/4有最小值。 (感觉x的取值范围是不是有个等号?)

你应该试着,把题目写在纸上,然后拍照上传来提问。 这样很难让人看的懂。 问问题就该专业点。

f(x)=(cosx)^4-2sinxcosx-(sinx)^4 =[(cosx)^2+(sinx)^2][(cosx)^2-(sinx)^2]-2sinxcosx =(cosx)^2-(sinx)^2-2sinxcosx =cos(2x)-sin(2x) = √2*[cos(2x)*√2/2-sin(2x)*√2/2] = √2*[cos(2x)cos(π/4)-sin(2x)sin(π/4)] = √2cos(2x+π/4) 。 (2)因...

分子分母都除以cos^2x f(x)=cos^2 x/cos xsin x-sin^2 x =1/[tanx-(tanx)^2] =1/[-(tanx-1/2)^2+1/4] 当tanx=1/2时 函数有最小值为4

f(x)=sin²x+2sinxcosx+3cos²x =(1-cos2x)/2+sin2x+3(1+cos2x)/2 =√2sin(2x+π/4)+2 (I) 函数f(x) 的最小正周期T=2π/2=π ∵x∈(0,π) ∴2x+π/4∈(π/4,9π/4) 当2x+π/4=π/2.即x=π/x时,f(x)=2+√2为最大值, 当2x+π/4=3π/2.即x=5π/8时,f(x)...

f(x)=2sinxcosx-sin²x+cos²x =sin2x+cos2x =√2sin(2x+π/4) 在[0, π]上,2x+π/4∈[π/4, 2π+π/4] 其中单调增区间为: 2x+π/4 ∈[π/4, π/2]U[3π/2,9π/4] 单调减区间: 2x+π/4 ∈[π/2, 3π/2] 即f(x)的单调增区间为:[0, π/8]U[5π/8, π] f(x)...

解: (1) f(x)=cos²x-√3sinxcosx+½ =½[1+cos(2x)]-(√3/2)sin(2x)+½ =½cos(2x)-(√3/2)sin(2x)+1 =cos(2x+π/3)+1 最小正周期T=2π/2=π cos(2x+π/3)=1时,f(x)取得最大值f(x)max=1+1=2 cos(2x+π/3)=-1时,f(x)取得最小值f(...

f(x)=sinxcosx+√3(cosx)^2-√3/2 =(1/2)sin2x+(√3/2)cos2x =sin2xcosπ/3+cos2xsinπ/3 =sin(2x+π/3) 1. 0

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