tan(x+π/4)-tan(x-π/4)
=(tanx+tan(π/4))/(1-tanx*tan(π/4))-(tanx-tan(π/4))/(1+tanx*tan(π/4))
=(tanx+1)/(1-tanx)-(tanx-1)/(1+tanx)
=((tanx+1)²+(tanx-1)²)/(1-tan²x)
=2(tan²x+1)/(1-tan²x)