How do you Simplify (1+ tanx) / (1- tanx)

Answer: Consider the following: (1 + tan x) / (1 – tan x) ———-(1)

Based on trigonometric identities,

[(tan A + tan B) / 1 – tan A tan B] = tan (A + B).

We know that tan (π / 4) = 1.

As a result, equation (1) may be written as

(tan (π / 4)+ tan x) / (tan (π / 4) – tan x) ———-(2)

We may write equation (2) as tan (x + (π / 4) since tan (π / 4) = 1.

As a result, the formula (1 + tan x) / (1 – tan x) may be reduced to tan (x + (π / 4)).