设向量a=(根号3coswx^2,sinwx),b=(1,coswx)（其中w>o),已知f(x)=向量a*向量-根号3

1)
(f(x)=向量a*向量-根号3/2.
=√3cos²wx+sinwxcoswx-√3/2
=√3/2(1+cos2wx)+1/2*sin2wx-√3/2
=1/2*sin2wx+√3/2*cos2wx
=sin(2wx+π/3)
∵f(x)最小正周期为2π
∴2π/(2w)=2π
∴w=1/2
f(x)=sin(x+π/3)

(2)f(α）=3/5,f(β）=-4/5
∴sin(α+π/3)=3/5,sin(β+π/3)=-4/5
∵α属于（π/6,2π/3）
,∴α+π/3∈(π/2,π)
∴cos(α+π/3)=-4/5
∵β属于（-5π/6,-π/3)
∴β+π/3∈(-π/2,0)
∴cos(β+π/3)=3/5
cos(α-β）=cos[(a+π/3)-(β+π/3)]
=cos(α+π/3)cos(β+π/3)+sin(α+π/3)sin(β+π/3)
=-4/5*3/5+3/5*(-4/5)
=-24/25