已知函数f(x)=2cosxsin(x+π/3)-根号3sin^2x+sinxcosx+2(x∈R),1,求函数f(x)的最小正周期和单调增区间;

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已知函数f(x)=2cosxsin(x+π/3)-根号3sin^2x+sinxcosx+2(x∈R),1,求函数f(x)的最小正周期和单调增区间;

已知函数f(x)=2cosxsin(x+π/3)-根号3sin^2x+sinxcosx+2(x∈R),1,求函数f(x)的最小正周期和单调增区间;
已知函数f(x)=2cosxsin(x+π/3)-根号3sin^2x+sinxcosx+2(x∈R),
1,求函数f(x)的最小正周期和单调增区间;

已知函数f(x)=2cosxsin(x+π/3)-根号3sin^2x+sinxcosx+2(x∈R),1,求函数f(x)的最小正周期和单调增区间;
f(x)=sinxcosx+sqrt(3)(cosx)^2-sqrt(3)(sinx)^2+sinxcosx+2
=2sinxcosx+sqrt(3)[(cosx)^2-(sinx)^2]
=sin2x+sqrt(3)cos2x
=2sin(2x+π/3)
所以最小正周期是π
单调增区间[-5π/12+kπ,π/12+kπ],k是整数.

原式=2cosx(sinx/2+√3*sinx/2)-√3*(sinx)^2+sinxcosx+2
=2sinxcosx+√3(cos^2(x)-sin^2(x))+2
=sin2x+√3cos2x+2
=2sin(2x+π/3)+2
所以最小正周期是π,单调增区间为[-5π/12+kπ,π/12+kπ],k为整数