已知向量a=(根号3sinx,cosx),b=(cosx,cosx),函数f(x)=2a·b-1

f(x)=2a*b－1
=2[√3sinxcosx＋cos²x]－1
=(√3)sin2x＋[1＋cos2x]－1
=2[(√3/2)sin2x＋(1/2)cos2x]
=2[sin2xcos(π/6)＋cos2xsin(π/6)]
=2sin(2x＋π/6)
则：f(x)=1就是2sin(2x＋π/6)=1
sin(2x＋π/6)=1/2
因x∈[π/6,π/2],则2x＋π/6∈[π/2,7π/6],则：2x＋π/6=5π/6,得：x=π/3