Question

How do you simplify `(sec^2x-1)/(secx-1)`?

Answer 1

`secx+1`

Explanation:

The numerator is a `color(blue)"difference of squares"` and is factorised, in general, as shown.

`color(red)(bar(ul(|color(white)(2/2)color(black)(a^2-b^2=(a-b)(a+b))color(white)(2/2)|)))`

`"here "a=secx" and "b=1`

`rArrsec^2x-1=(secx-1)(secx+1)`

`rArr(sec^2x-1)/(secx-1)`

`=(cancel((secx-1)^1)(secx+1))/cancel(secx-1)^1`

`=secx+1`