Question

How do you simplify `cos 2x = (1-tan^2x)/(1+tan^2x)`?

Answer 1

Kindly go through a Proof in the Explanation.

Explanation:

We have, `cos2x=cos^2x-sin^2x=(cos^2x-sin^2x)/1`,

`=(cos^2x-sin^2x)/(cos^2x+sin^2x)`,

`=[cos^2x{1-sin^2x/cos^2x}]/[cos^2x{1+sin^2x/cos^2x}]`.

`rArr cos2x=(1-tan^2x)/(1+tan^2x)`, as desired!