Precalculus Examples

$\frac{1 - \sec^{2} (x)}{\tan^{2} (x)}$

Step 1

Simplify with factoring out.

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Step 1.1

Reorder $1$ and $- \sec^{2} (x)$ .

$\frac{- \sec^{2} (x) + 1}{\tan^{2} (x)}$

Step 1.2

Factor $- 1$ out of $- \sec^{2} (x)$ .

$\frac{- (\sec^{2} (x)) + 1}{\tan^{2} (x)}$

Step 1.3

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{- \sec^{2} (x) - 1 \cdot - 1}{\tan^{2} (x)}$

Step 1.4

Factor $- 1$ out of $- \sec^{2} (x) - 1 \cdot - 1$ .

$\frac{- (\sec^{2} (x) - 1)}{\tan^{2} (x)}$

Step 2

Apply pythagorean identity.

$\frac{- \tan^{2} (x)}{\tan^{2} (x)}$

Step 3

Cancel the common factor of $\tan^{2} (x)$ .

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Step 3.1

Cancel the common factor.

$\frac{- \tan^{2} (x)}{\tan^{2} (x)}$

Step 3.2

Divide $- 1$ by $1$ .

$- 1$