How do you simplify (1 - tan²(x)) /( 1 + tan²(x))?

We’ll use trigonometric identity 1 + tan²x = sec²x for simplifying (1 - tan²(x)) /(1 + tan²(x))

Answer: (1 - tan²(x)) /(1 + tan²(x)) = cos 2x

Let’s find the simplified form of (1 - tan²(x)) /( 1 + tan²(x))

Explanation: 

We have  to simplify the trigonometric expression (1 - tan²(x)) /( 1 + tan²(x))

We know from trigonometric identity that 1 + tan²x = sec²x

Hence, the given expression becomes (1 - tan²(x)) /(sec²(x))

We know that, 1 / sec x = cos x and tan x = sin x / cos x.

So, we can write it as:

(1 - tan²(x)) / (sec²(x)) = 1/sec²x - tan²(x)/sec²(x)

= cos²x – (sin²x cos²x) / cos²x

= cos²x – sin²x

= cos 2x

Thus, (1 - tan²(x)) /(1 + tan²(x)) = cos 2x