Precalculus Examples

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

Step 1

Apply pythagorean identity.

$\frac{1}{\sin^{2} (x)}$

Step 2

Simplify with factoring out.

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Step 2.1

Rewrite $1$ as $1^{2}$ .

$\frac{1^{2}}{\sin^{2} (x)}$

Step 2.2

Rewrite $\frac{1^{2}}{\sin^{2} (x)}$ as ${(\frac{1}{\sin (x)})}^{2}$ .

${(\frac{1}{\sin (x)})}^{2}$

Step 3

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$\csc^{2} (x)$