Precalculus Examples

$\frac{\sec (x) \cos (x)}{\tan (x)}$

Step 1

Separate fractions.

$\frac{\cos (x)}{1} \cdot \frac{\sec (x)}{\tan (x)}$

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

Cancel the common factor of $\cos (x)$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

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

Step 6

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

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

Step 7

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

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

Step 8

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

$\cot (x)$