How do you simplify (1 + tan x) / (1 - tan x)?

We can simplify the above expression by using tangent formulas of trigonometry identities.

Answer: Expression (1 + tan x) / (1 - tan x) can be simplified as tan (x + (π / 4))

Let us solve this problem step by step.

Explanation:

Let us consider (1 + tan x) / (1 - tan x) -------(1)

From trigonometric identities,

tan (A + B) = [(tan A + tan B) / 1 - tan A × tan B]

We know, tan (π / 4) = 1

Therefore, equation (1) can be written as 

(tan (π / 4) + tan x) / (1 - tan (π / 4) × tan x) -------(2)

Since, tan (π / 4) = 1, we can write equation (2) as tan (x + (π / 4)).

Hence, expression (1 + tan x) / (1 - tan x) can be simplified as tan (x + (π / 4)).