f(x)=2cos^2x-1+2根号3sinxcosx
=cos2x+根号3sin2x
=2(1/2cos2x+根号3/2sin2x)
=2sin(2x+π/6)
0≤x≤π/2
0≤2x≤π
π/6≤2x+π/6≤7π/6
-1/2≤sin(2x+π/6)≤1
-1≤2sin(2x+π/6)≤2
值域[-1,2]