化简tan(x+π/4)-tan(x-π/4)

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)

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

=(tanx+1)/(1-tanx)+(1-tanx)/(1+tanx)
=[(1+tanx)^2+(1-tanx)^2]/1-(tanx)^2
=2*[1+(tanx)^2]/[1-(tanx)^2]

要化简到什么程度。利用公式拆开，通分不能算结束么？