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# How do you simplify (1 - tan^{2}(x)) /( 1 + tan^{2}(x))?

We’ll use trigonometric identity 1 + tan^{2}x = sec^{2}x for simplifying (1 - tan^{2}(x)) /(1 + tan^{2}(x))

## Answer: (1 - tan^{2}(x)) /(1 + tan^{2}(x)) = cos 2x

Let’s find the simplified form of (1 - tan^{2}(x)) /( 1 + tan^{2}(x))

**Explanation: **

We have to simplify the trigonometric expression (1 - tan^{2}(x)) /( 1 + tan^{2}(x))

We know from trigonometric identity that 1 + tan^{2}x = sec^{2}x

Hence, the given expression becomes (1 - tan^{2}(x)) /(sec^{2}(x))

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

So, we can write it as:

(1 - tan^{2}(x)) / (sec^{2}(x)) = 1/sec^{2}x - tan^{2}(x)/sec^{2}(x)

= cos^{2}x – (sin^{2}x cos^{2}x) / cos^{2}x

= cos^{2}x – sin^{2}x

= cos 2x

### Thus, (1 - tan^{2}(x)) /(1 + tan^{2}(x)) = cos 2x

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