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

#### Solution

Consider

$\frac{1+tan x}{1-tan x}$………………………..(1)

We know that

$tan(A+B)=\frac{tanA + tanB}{1-tanAtanB}$

and also

$tan(\frac{\Pi }{4})= 1$

Hence equation (1) becomes

$\frac{tan \frac{\pi }{4} + tan x}{1-tan\frac{\pi }{4} tanx}$

since $tan\left ( \frac{\pi}{4} \right ) = 1$

⇒ $tan\left ( x +\frac{\pi}{4} \right )$

∴  $\frac{1+tanx}{1-tanx}= tan\left ( x+\frac{\pi}{4} \right )$