Simplify (tan(x)^2+1)/(cot(x)^2-csc(x)^2)

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

Step 1

Apply pythagorean identity.

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

Step 2

Simplify with factoring out.

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

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

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

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

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

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

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.

Multiply $- 1$ by $1$ .

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

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

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

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

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