(1) f(x)=2cosxsin(x-π/3)+√3 sin^2x+sinxcosx
=2cosx[1/2sinx-√3/2cosx)+√3/2[1-cos2x]+1/2sin2x
=1/2sin2x-√3cos^2x-√3/2cos2x+1/2sin2x+√3/2
=sin2x-√3/2cos2x-√3/2cos2x+√3/2-√3/2
=sin2x-√3cos2x
=2sin(2x-π/3)
函数y=f（x）图像的对称中心:(π/6,0)
(2) 4sin(2x-π/3)-m+1 在【π/6,7π/12】有两个相异的实根
当x=π/6时， 4sin(2x-π/3)-m+1=-m+1
当x=7π/12时， 4sin(2x-π/3)-m+1=4sin(5π/6)-m+1=2-m+1=3-m
(4sin(2x-π/3)-m+1)'=8cos(2x-π/3)=0 x=5π/12
当x0; 当x>5π/12时，导数0 且 -m+1