Precalculus Examples

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

Step 1

Separate fractions.

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

Step 2

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

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

Step 3

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

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

Step 4

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\sin (x)}$ .

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

Step 5

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

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

Step 6

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

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

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

Step 7

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

$\sec (x) \cos (x)$

Step 8

Rewrite in terms of sines and cosines, then cancel the common factors.

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Step 8.1

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

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

Step 8.2

Cancel the common factors.

$1$