Precalculus Examples

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

Step 1

Separate fractions.

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

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

Step 6

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

$\sec (x) \sin (x)$

Step 7

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

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

Step 8

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

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

Step 9

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

$\tan (x)$