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设函数Fx等于4sinx(Cos%sinx)加3 1.当x属于(0,派...

f(x) = 4sinx(cosx-sinx)+3 = 4sinxcosx-4sin²x+3 = 2sin2x-2(1-cos2x)+3 = 2sin2x+2cos2x+1 = 2√2(sin2xcosπ/4+cos2xsinπ/4) + 1 = 2√2sin(2x+π/4) + 1 x∈(0,π) 2x∈(0,2π) 2x+π/4∈(π/4,9π/4) 2x+π/4∈(π/2,3π/2)时单调递减 此...

1.令t=sinx, 则0=

参考

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)...

f(x)=4√3sinxcosx-4cos²x+1 =2√3sin(2x)-2[cos(2x)+1]+1 =2√3sin(2x)-2cos(2x) -1 =4[sin(2x)(√3/2)-cos(2x)(1/2)] -1 =4sin(2x -π/6) -1 x∈[0,π/2] 0-π/6≤2x-π/6≤2·(π/2) -π/6 -π/6≤2x-π/6≤5π/6 -1/2≤sin(2x-π/6)≤1 4×(-1/2)-1≤4sin(2x -...

f(x)=cos(2x+π/3)+2sin^2(x) =cos(2x)cos(π/3)-sin(2x)sin(π/3)+[1-cos(2x)] =(1/2)cos(2x)-(√3/2)sin2x+1-cos(2x) = - [(√3/2)sin2x+(1/2)cos(2x)]+1 = - sin(2x+π/6)+1 在正弦函数前面加了一负号后单调性与没有负号的单调性相反, 欲求单调减...

fx=sinxcos(x+派/3)+根号3/4 =sinx【1/2cosx-根号3/2sinx】 =1/4sin2x-根号3/2sinx平方 =1/4sin2x-根号3/4(2sinx平方) =1/4sin2x-根号3/4(1-cos2x) =1/2(1/2sin2x+根号3/2cos2x)-根号3/4 =1/2sin(2x+派/3)-根号3/4 。。。

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

用升幂公式:cos2x=(cosx)^2-(sinx)^2=2(cosx)^2-1 f(x)=[2*(cos^2)+8*(sin^2)]/(2sinx*cosx)=(1+4tan^2)/tan =(1/tanx)+4*tanx>=2*根号[(1/tanx)*4tanx]=4 所以最小值为4 追问: 麻烦问下2*根号[(1/tanx)*4tanx]怎么推出来呢啊?

(1)函数f(x)=4sinx?sin 2 ( π 4 + x 2 )+cos2x=2sinx[1-cos( π 2 +x )]+cos2x=2sinx+2sin 2 x+cos 2 x-sin 2 x=1+2sinx…(4分)由题意需[- π 2 , 2π 3 ] ?[- π 2ω , π 2ω ] 得ω ∈(0, 3 4 ] …(6分)(2)由题意当 π 6 ≤x≤ 2π 3 时,...

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