f(x)=sinx/2×cosx/2+cos^2x/2- 1/2= 1/2sinx+( 1+cosx)/2- 1/2= 1/2sinx+ 1/2cosx=√2/2sin(x+π/4)

( 1)f(a)=√2/2 sin(a+π/4)=√2/4

Sin(a+π/4)= 1/2 is obtained.

And a belongs to (0, π), so a+π/4 belongs to (π/4, 5π/4).

So a+π/4=5π/6 gives a=7π/ 12.

(2)x belongs to [-π/4, π], so x+π/4 belongs to [0,5 π/4] SIN (X+π/4) belongs to [-√2/2, 1].

F(x) belongs to [- 1/2, √2/2].

So the maximum value of the function is √2/2, and the minimum value is-1/2.