y=3/2cosx-根号3/2sinx
=√3(sin(π/3)cosx-cos(π/3)sinx)
=√3sin(π/3-x)
x∈(0,π/2),
所以,π/3-x∈(-π/6,π/3)
x＝π/2时,y＝-√3/2
x＝0时,y＝3/2
所以,y的值域为(-√3/2,3/2)