已知函数f(x)=sin(2x+π/3)+sin(2x-π/3)+2cos^2x,x∈R,求f（x）的最小正周期

f(x)=sin(2x+π/3)+sin(2x-π/3)+2cos^2x=2sin[(2x+π/3+2x-π/3)/2]cos[(2x+π/3-2x+π/3)/2]+cos2x+1=2sin(2x)cosπ/3+cos2x+1=sin2x+cos2x+1=√2(√2/2sin2x+√2/2cos2x)+1=√2sin(2x+π/4)+1∴最小正周期T=2π/2...