答案：√2/10
解：∵α∈(0,π/2),∴α+π/6∈(π/6,2π/3)
∵cos(α+π/6)=3/5,∴sn(α+π/6)=4/5
∴sin(α-π/12)
=sin[(α+π/6)- π/4]
= sin(α+π/6)cos(π/4)- sin(α+π/6)cos(π/4)
=4/5×√2/2-3/5×√2/2
=√2/10
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