Question

How do you simplify `sec^4x + sec^2x - 2`?

Answer 1

`=( tan^2x+3)(tan^2x)`

Explanation:

`sec^4x + sec^2x - 2`

`=sec^4x + 2sec^2x -sec^2x- 2`

`=sec^2x( sec^2x+ 2) -1(sec^2x+2)`

`=( sec^2x+ 2)(sec^2x -1)`

`=( tan^2x+1+ 2)(tan^2x+1-1)`

`=( tan^2x+3)(tan^2x)`