Algebra Examples

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

Step 1

Apply pythagorean identity.

$\frac{\sec^{2} (x)}{\cot^{2} (x) - \csc^{2} (x)}$

Step 2

Simplify with factoring out.

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Step 2.1

Reorder $\cot^{2} (x)$ and $- \csc^{2} (x)$ .

$\frac{\sec^{2} (x)}{- \csc^{2} (x) + \cot^{2} (x)}$

Step 2.2

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

$\frac{\sec^{2} (x)}{- (\csc^{2} (x)) + \cot^{2} (x)}$

Step 2.3

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

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

Step 2.4

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

$\frac{\sec^{2} (x)}{- (\csc^{2} (x) - \cot^{2} (x))}$

Step 3

Apply pythagorean identity.

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

Step 4

Simplify the expression.

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Step 4.1

Multiply $- 1$ by $1$ .

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

Step 4.2

Move the negative one from the denominator of $\frac{\sec^{2} (x)}{- 1}$ .

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

Step 4.3

Rewrite $- 1 \cdot \sec^{2} (x)$ as $- \sec^{2} (x)$ .

$- \sec^{2} (x)$