Question

Prove that `(1+tan^2x)cos^2x=1`?

Answer 1

See below

Explanation:

We will use the following identities

`cos^2x+sin^2x=1`

`sec^nx=1/cos^nx`

`tan^nx=sin^nx/cos^nx`

Proof

We start by manipulating the first identity

`cos^2x+sin^2x=1`

`rArr cos^2/cos^2x+sin^2x/cos^2x=1/cos^2x`

`rArr1+tan^2x=sec^2x`

So

`(1+tan^2x)cos^2x=sec^2xcos^2x=1/cos^2xcos^2x=1` `color(white)(aaaa)square`