tan(α+π/4)+tan(α-π/4)
=tan(α+π/4+α-π/4)[1-tan(α+π/4)tan(α-π/4)]
=tan2α[1-tan(α+π/4)tan(α+π/4-π/2)]
=tan2α[1+tan(α+π/4)cot(α+π/4)]
=tan2α[1+1]
=2tan2α
得证