(1)f(x)=4cos(x/2)[(√3/2)cos(x/2)-(1/2)sin(x/2)]
=2√3[cos(x/2)]^2-2sin(x/2)cos(x/2)
=√3(1+cosx)-sinx
=√3+2cos(x+π/6),
它的周期=2π,
由x+π/6=(k+1/2)π,k∈Z得x=(k+1/3)π,
y=f(x)的图像的对称中心坐标为((k+1/3)π,√3).
(2)f(C)=√3+2cos(C+π/6)=√3+1,
∴cos(C+π/6)=1/2,
解得C=π/6.
由正弦定理,a=ABsinA/sinC=2sinA,同理,b=2sinB,
∴△ABC的面积=√3/2=（1/2）absinC=sinAsinB
=(1/2)[cos(A-B)-cos(A+B)]
=(1/2)[cos(A-B)+cosC]
=(1/2)[cos(A-B)+√3/2],
∴cos(A-B)=√3/2,
∴A-B=土π/6,A+B=5π/6,
∴(A,B)=(π/2,π/3)或(π/3,π/2),
∴a=2,b=√3;或a=√3,b=2.