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

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#### Explanation

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#### Explanation:

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41
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:

${\sec}^{2} x - {\tan}^{2} x = \frac{1}{\cos} ^ 2 x - {\sin}^{2} \frac{x}{\cos} ^ 2 x$

$\textcolor{w h i t e}{{\sec}^{2} x - {\tan}^{2} x} = \frac{1 - {\sin}^{2} x}{\cos} ^ 2 x$

$\textcolor{w h i t e}{{\sec}^{2} x - {\tan}^{2} x} = {\cos}^{2} \frac{x}{\cos} ^ 2 x$

$\textcolor{w h i t e}{{\sec}^{2} x - {\tan}^{2} x} = 1$

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