已知函数f（x）=sin（x/2）cos（x/20+cos²x/2-1/2,若f（a）=根号2/4,a∈（0,π）,求a的值

f（x）=sin（x/2）cos（x/2)+cos²x/2-1/2
=1/2sinx-1/2cosx
=√2/2sin(x-π/4)
f（a）=√2/4=√2/2sin(a-π/4)
sin(a-π/4)=1/2
a-π/4=π/6或5π/6 (舍去)
a=5π/12