Precalculus Examples

$\frac{\cos (x) \cdot \csc (x)}{\tan (x)}$

Separate fractions.

$\frac{\csc (x)}{1} \frac{\cos (x)}{\tan (x)}$

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

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

Multiply by the reciprocal of the fraction to divide by $\frac{\sin (x)}{\cos (x)}$ .

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

Write $\cos (x)$ as a fraction with denominator $1$ .

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

Simplify.

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

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

Write $\cos (x)$ as a fraction with denominator $1$ .

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

Multiply $\frac{\cos (x)}{1}$ and $\frac{\cos (x)}{\sin (x)}$ .

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

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

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

Multiply the numerator by the reciprocal of the denominator.

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

Multiply $\frac{1}{\sin (x)}$ by $1$ .

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

Simplify the numerator.

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Raise $\cos (x)$ to the power of $1$ .

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

Raise $\cos (x)$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $1$ .

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

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

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

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

Raise $\sin (x)$ to the power of $1$ .

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

Raise $\sin (x)$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $1$ .

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

Convert from $\frac{\cos^{2} (x)}{\sin^{2} (x)}$ to $\cot^{2} (x)$ .

$\cot^{2} (x)$

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