已知函数f(x)=sin(2x+π/6)+sin(2x-π/6)+2cos²x

(1)f(x)
＝sin(2x＋π/6)＋sin(2x－π/6)＋2cos²x
＝sin2xcosπ/6＋cos2xsinπ/6＋sin2xcosπ/6－cos2xsinπ/6＋2cos²x
＝2sin2xcosπ/6＋2cos²x
＝√3sin2x＋cos2x＋1
＝2sin(2x＋π/6)＋1
∵－1≤sin(2x＋π/6)≤1
∴f(x)max＝1×2＋1＝3
最小正周期T＝2π/ω＝2π/2＝π
(2)
f(x)＝2sin(2x＋π/6)＋1≥2
即：2sin(2x＋π/6)≥1
sin(2x＋π/6)≥1/2
∴π/6＋2kπ≤2x＋π/6≤5π/6＋2kπ
即：{ x | kπ≤x≤π/3＋kπ,k∈Z}