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

By K Balaji|Updated : November 9th, 2022

(1 + tan x)/ (1 - tan x) = tan (π/4 + x)

The three basic categories of trigonometric functions are cosine, sine, and tangent. And from the basic functions, one can deduce the three secant, cotangent, and cosecant functions. In contrast to the fundamental trigonometric functions, the other three functions are essentially employed more frequently.

Simplify the required term.

We know that, tan (π/4) = 1

So (1 + tan x)/ (1 - tan x) can be written as [tan (π/4) + tanx]/ [tan (π/4) - tan x]

We know that tan (A + B) = tan A + tan B/ 1 - tan A tan B

= tan (π/4) + tan x/ 1 - tan (π/4) tan x

On simplifying we get

= tan (π/4 + x)

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Tan function

The ratio of the lengths of the adjacent and opposing sides is known as the tangent function. It has to be observed that the ratio of sine and cosine to the tan can also be used to express the tan. The following will be the tan function based on the diagram that was obtained above.

Tan a = Opposite/Adjacent = CB/BA

In terms of sine and cos, tan is also equivalent to:

Tan a = sin a/cos a

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