Question

How do you factor the expression and use the fundamental identities to simplify `sec^3x-sec^2x-secx+1`?

Answer 1

`sec^3x-sec^2x-secx+1=tan^2x(secx-1)`

Explanation:

`sec^3x-sec^2x-secx+1`

= `sec^3x-secx-sec^2x+1`

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

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

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