(1)T/4=π/3-π/12=π/4==>T=π==>w=2π/T=2，A=1
∴f(x)=sin(2x+φ)
f(π/12)=sin(π/6+φ)=1==>π/6+φ=π/2==>φ=π/3
∴f(x)=sin(2x+π/3)
(2)∵f(α+π/12)=1/3(α∈(0,π/2))
f(α+π/12)= sin(2α+π/6+π/3)=cos2α=1/3
∴sin2α=2√2/3
Tanα=(sin2α)/(1+cos2α)= √2/2
∴f(x)=sin(2x+φ)
f(π/12)=sin(π/6+φ)=1==>π/6+φ=π/2==>φ=π/3
∴f(x)=sin(2x+π/3)
(2)∵f(α+π/12)=1/3(α∈(0,π/2))
f(α+π/12)= sin(2α+π/6+π/3)=cos2α=1/3
∴sin2α=2√2/3
Tanα=(sin2α)/(1+cos2α)= √2/2
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