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

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Answer 1 · 2017-01-25T14:32:27

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

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

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

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

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

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

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