f(x)=√2sin(x+π/4)
∵x∈(0,π/2)
∴x+π/4∈（π/4,π/2）
∴sin(x+π/4) ∈(√2/2,1]
∴√2sin(x+π/4) ∈(1,√2]
即函数值域为(1,√2]