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

1 Answer
George C.
Sep 3, 2016

sec^2 x - tan^2 x = 1

Explanation:

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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