已知函数f(x)=[2sin(x-π/6)+√3sin x]cos x+sin^2x,x∈R

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已知函数f(x)=[2sin(x-π/6)+√3sin x]cos x+sin^2x,x∈R

已知函数f(x)=[2sin(x-π/6)+√3sin x]cos x+sin^2x,x∈R
已知函数f(x)=[2sin(x-π/6)+√3sin x]cos x+sin^2x,x∈R
 

已知函数f(x)=[2sin(x-π/6)+√3sin x]cos x+sin^2x,x∈R
2sin(x-π/6)=2×[sinxcos(π/6)-cosxsin(π/6)]=√3sinx-cosx
则:
f(x)=cosx[√3sinx-cosx+√3sinx]+sin²x
f(x)=2√3sinxcosx-cos²x+sin²x
f(x)=2√3sinxcosx-(cos²x-sin²x)
f(x)=√3sin(2x)-cos(2x)
f(x)=2sin(2x-π/6)
(1)最小正周期是2π/2=π
(2)?

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