Question

How do you simplify `(sec^2x) - (tan^2x)`?

Answer 1

`sec^2 x - tan^2 x = 1`

Explanation:

Note that:

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

Hence:

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

and we find:

`sec^2 x - tan^2 x = 1/cos^2 x - sin^2 x/cos^2 x`

`color(white)(sec^2 x - tan^2 x) = (1 - sin^2 x)/cos^2 x`

`color(white)(sec^2 x - tan^2 x) = cos^2 x/cos^2 x`

`color(white)(sec^2 x - tan^2 x) = 1`