2. Calculate the value range of y=sin(2x+π/6) at x ∈ [π/4,3 π/4], where 2x+π/6 ∈ [π 2/3,5 π/3], and then y ∈ [-/kloc-0]. When a < 0, f(x) is a decreasing function, and f(- 1)= root number 3- 1, f (root number 3 /2)= -3, a=- 1 b= root number 3- 1.

3. Simplify to get the square of y =-cosx+acosx+5a/8-1/2cosx ∈ [0, 1].

The image of this function is a parabola with a downward opening and the symmetry axis is a/2. It is discussed in three situations.

① a/2 < 0 when cosx=0, take the maximum value of y and bring it into the original formula to get a = 12/5 > 0, and discard it.

②0≤a/2≤ 1。 At this time, y has the maximum value when cosx=a/2, and the square of A +5a/2-6=0 is brought to get a=3/2 or a=-4. Because 0≤a/2≤ 1, a=3/2.

③ A/2 > 1, when cosx= 1, y takes the maximum value, which is brought into the original formula to get 13a/8 = 5/2, and A = 20/ 13. Discard because a/2 > 1.

To sum up, a=3/2.