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
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