f(x)=2cos*sin(x+π/3)-^3sin^2x+sinx*cosx1.求函数最小正周期2.求函数最大最小值3.求f（x）的递增区间

f(x)=2cos*sin(x+π/3)-^3sin^2x+sinx*cosx1.求函数最小正周期2.求函数最大最小值3.求f（x）的递增区间
f(x)=2cos*sin(x+π/3)-^3sin^2x+sinx*cosx
1.求函数最小正周期
2.求函数最大最小值
3.求f（x）的递增区间

f(x)=2cos*sin(x+π/3)-^3sin^2x+sinx*cosx1.求函数最小正周期2.求函数最大最小值3.求f（x）的递增区间
f(x)=2cos*sin(x+π/3)-^3sin^2x+sinx*cosx
=2cosx(1/2sinx+√3/2cosx)-^3sin^2x+sinx*cosx
=sin2x+√3cos2x
=2sin(2x+π/3)
1.T=2π/2=π.
2.最大值2,最小值-2.
3.2kπ -π/2≤2x+π/3≤2kπ+π/2,
2kπ -5π/6≤2x+≤2kπ+π/6,
kπ -5π/12≤x≤kπ+π/12,
f（x）的递增区间是[kπ -5π/12,kπ+π/12]k∈Z.