=√3sinx·cosx-sin^2x·+√3sinx·cosx+cos²x
=√3sin2x+cos2x
=2(√3/2sin2x+1/2cos2x )
=2sin(2x+π/6)
最大值=2
x=Kπ+π/6
2)0≤x≤π/2
π/6≤2x+π/6≤7π/6
f(x)取值范围-1,2[]
已知函数f(x)=2sinx·sin(π\/3-x)+√3sinx·cosx+cos²x (1)求函数...
f(x)=2sinx·sin(π\/3-x)+√3sinx·cosx+cos²x =√3sinx·cosx-sin^2x·+√3sinx·cosx+cos²x =√3sin2x+cos2x =2(√3\/2sin2x+1\/2cos2x )=2sin(2x+π\/6)最大值=2 x=Kπ+π\/6 2)0≤x≤π\/2 π\/6≤2x+π\/6≤7π\/6 f(x)取值范围-1,2[]
已知函数f(x)=2sinxsin(x+π\/3) 求函数f(x)的最大值
=2sinx(1\/2*sinx+√3\/2*cosx)=sin²x+√3sinxcosx =(1-cos2x)\/2+√3\/2sin2x =1\/2+√3\/2*sin2x-1\/2*cos2x =1\/2+sin(2x-π\/6)所以函数f(x)的最大值是1\/2+1=3\/2
已知f(x)=2sinx cosx+2√3cos²x—√3,x∈[0,π\/2] (1)求f(x)最大
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已知函数f(x)=2sinx(cosx+sinx)(x∈R)求f(x)在区间【0,π】上的最大...
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已知函数f(x)=2sinxcos(π\/2-x)-√3sin(π+x)cosx+sin(π\/2+x)cosx...
=2sin^2x+√3\/2*sin2x+cos^2x =sin^2x+√3\/2*sin2x+1 =(1-cos2x)\/2+√3\/2*sin2x+1 =√3\/2*sin2x-1\/2cos2x+1\/2+1 =√3\/2*sin2x-1\/2cos2x+3\/2 =sin2xcosπ\/6-cos2xsinπ\/6+3\/2 =sin(2x-π\/6)+3\/2 T=2π\/2=π -1<=sin(2x-π\/6)<=1 1\/2<=sin(2x...
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已知函数f(x)=2sinx(sinx+cosx) (1)求f(x)的最小正周期和最大值】
f（x）=2sinx(sinx+cosx)=2sin²x+2sinxcosx=1-cos2x+sin2x =1+√2sin(2x-π\/4)（1）f（x）的最小正周期T=2π\/2=π 最大值为1+√2 （2）画出y=f（x）在区间（-兀\/2，兀\/2）的图像，如图
已知函数f(x)=2sinx(sinx+cosx)(1)求f(x)的最小正周期和最大值
f(x)=2sinx(sinx+cosx)=2sin²x+2sinxcosx =1-cos2x+sin2x =1+√2 （√2\/2sin2x-√2\/2cos2x）=1+√2（sin2xcosπ\/4-cos2xsinπ\/4）=1+√2sin(2x-π\/4)所以 最小正周期=π 最大值=1+√2
【数学】已知函数f(x)=2cosxsin(x+π\/3)-√3sin^2(x)+sinxcosx
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已知函数f(x)=2cosxsin(x+π\/3)+sinxcosx-√3sin²x,x∈R
=2 sinxcosx+√3(cos²x-sin²x)=sin2x+√3cos2x =2sin(2x+π\/3)(1)最小正周期 =2π\/2=π （2）x∈[0,5π\/12]2x+π\/3∈[π\/3,7π\/6]sin(2x+π\/3)∈[-1\/2,1]2sin(2x+π\/3)∈[-1,2]f（x）＞m成立 m<-1 如果您认可我的回答，请点击“采纳为满意...
