# How do you simplify #(sec^2x) - (tan^2x)#?

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George C.
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Sep 3, 2016

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Note that:

#sin^2 x + cos^2 x = 1#

Hence:

#cos^2 x = 1 - sin^2 x#

and we find:

#sec^2 x - tan^2 x = 1/cos^2 x - sin^2 x/cos^2 x#

#color(white)(sec^2 x - tan^2 x) = (1 - sin^2 x)/cos^2 x#

#color(white)(sec^2 x - tan^2 x) = cos^2 x/cos^2 x#

#color(white)(sec^2 x - tan^2 x) = 1#

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