Trigonometry Examples

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

Step 1

Simplify with factoring out.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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

Step 2

Apply pythagorean identity.

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

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

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

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

$\frac{1}{- 1}$

Step 3.1.3

Move the negative one from the denominator of $\frac{1}{- 1}$ .

$- 1 \cdot 1$

Step 3.2

Multiply $- 1$ by $1$ .

$- 1$