f(x)=2√3cos²x+2sinxcosx=√3(1+cos2x)+sin2x=√3cos2x+sin2x+√3=2sin(2x+π/3)+√3
1.f(x)=5√3/3,即2sin(2x+π/3)+√3=5√3/3,sin(2x+π/3)=√3/3,2x+π/3=2kπ+arcsin(√3/3),或者2x+π/3=(2k+1)π-arcsin(√3/3).∴{x|x=kπ-π/6-1/2arcsin(√3/3)或x=(k+1/2)π-π/6-1/2arcsin(√3/3)}
2.x∈[π/6,2π/3],