tan（α+π/4）+tan（α-π/4）=2tan2α

tan(α+π/4)+tan(α-π/4) ..用公式拆开
=(tanα+tanπ/4)/(1-tanαtanπ/4)+(tanα-tanπ/4)/(1+tanαtanπ/4) ..将tanπ/4写成1
=(1+tanα)/(1-tanα)+(tanα-1)/(1+tanα)
=(1+tanα)/(1-tanα)-(1-tanα)/(tanα+1) ..通分
=[(1+tanα)^2-(1-tanα)^2]/(1+tanα)(1-tanα) ..去括号
=[1+2tanα+(tanα)^2-1+2tanα-(tanα)^2]/(1+tanα)(1-tanα) ..约简
=4tanα/1^2-(tanα)^2
=2*[2tanα/1^2-(tanα)^2] ..代公式
=2tan2α