How do you simplify $( 1+ tanx) /( 1- tanx)$ ?

Question

151922 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-19T10:21:32

$(1+tanx)/(1-tanx)=tan(x+pi/4)$

We know that $tan(A+B)=(tanA+tanB)/(1-tanAtanB)$ and $tan(pi/4)=1$

Hence $(1+tanx)/(1-tanx)$

= $(tan(pi/4)+tanx)/(1-tan(pi/4)tanx$ , as $tan(pi/4)=1$

= $tan(x+pi/4)$

How do you simplify ( 1+ tanx) /( 1- tanx)( 1+ tanx) /( 1- tanx)?