How do you factor sec^2(x)-sec(x)+sin^2(x)*sec^2(x)?

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How do you factor sec^2(x)-sec(x)+sin^2(x)*sec^2(x)?

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Answer 1 · 2018-06-14T19:07:43

$sec^2x-secx+sin^2xsec^2x=-sec^2x(cosx+2)(cosx-1)$

Explanation:

Start by factoring out $-sec^2x$ to get
$-sec^2x(-1+1/secx-sin^2x)$
Using the fact that $secx=1/cosx$ and $sin^2x=1-cos^2x$ , we get
$-sec^2x(-1+cosx-1+cos^2x)$
Rearranging gives
$-sec^2x(cos^2x-cosx-2)$
Recognizing that this is a quadratic expression of $cosx$ , we can factor to get
$-sec^2x(cosx+2)(cosx-1)$

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How do you factor sec^2(x)-sec(x)+sin^2(x)*sec^2(x)?

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