Question

How do you show that `1 + tan^2x = sec^2x`?

Answer 1

Put on a common denominator:

`(cos^2x + sin^2x)/cos^2x= sec^2x`

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

`1/cos^2x= sec^2x`

Then use `1/cosx = secx`.

`sec^2x = sec^2x`

This has been proved.

Hopefully this helps!