(1) because the range of COS is (-1~ 1), and b >；; 0, that is, cos(2x+π/6)=- 1 takes the maximum value, and when its value is 1 takes the minimum value, a+b=3/2, a-b =-1/.

(2) Substituting the values of A and B to get -2sin(x-π/3)≥- 1, that is, sin(bx-π/3)≥ 1/2, then 3 π/4 ≤ x-π/3 ≤

13π/ 12≤x≤7π/ 12

If so, please adopt it!