Precalculus Examples

$1 - \cos^{2} (x) \csc (x)$

Step 1

Simplify each term.

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Rewrite $\csc (x)$ in terms of sines and cosines.

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

Combine $\frac{1}{\sin (x)}$ and $\cos^{2} (x)$ .

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

Step 2

Simplify each term.

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Factor $\cos (x)$ out of $\cos^{2} (x)$ .

$1 - \frac{\cos (x) \cos (x)}{\sin (x)}$

Separate fractions.

$1 - (\frac{\cos (x)}{1} \cdot \frac{\cos (x)}{\sin (x)})$

Convert from $\frac{\cos (x)}{\sin (x)}$ to $\cot (x)$ .

$1 - (\frac{\cos (x)}{1} \cot (x))$

Divide $\cos (x)$ by $1$ .

$1 - \cos (x) \cot (x)$