解
f(x)=2sinx/2(sinx/2+cosx/2)-1
=2sin²x/2+2sinx/2cosx/2-1
=sinx-(1-2sin²x/2)
=sinx-cosx
=√2sin(x-π/4)
∵-1≤sin(x-π/4)≤1
∴-√2≤f(x)≤√2
∴值域为[-√2,√2]
a∈(0,π)
f(a+π/4)=√2sin(a+π/4-π/4)=1
即sina=√2/2
∴a=π/4或a=3π/4