解方程：tan(x+π/4)+tan(x-π/4)=2cotx

化简：
（1+tanx)/(1-tanx)+(tanx-1)/(1+tanx)=2/tanx
4tanx/(1-tanx^2)=2/tanx
tanx^2=1/3

tanx=±√3/3

tan(x+π/4) = (1+ tanx)/(1 - tanx)
tan(x-π/4) = (tanx - 1)/(1 + tanx)
cotx = 1/tanx

相信后面的步骤一定难不住你了

(tanx+1)/(1-tanx)+(tanx-1)/(1+tanx)
=(tanx+1)^2-(tanx-1)^2/1-tanx^2
=4tanx/1-tanx^2
4tanx/1-tanx^2=2cotx=2/tanx
tanx=＋－√3/3

（1+tanx)/(1-tanx)+(tanx-1)/(1+tanx)=2/tanx
通分整理得：4tanx/(1-tanx^2)=2/tanx
tanx^2=1/3

tanx=±√3/3

x=±∏/6+k∏,k∈Z