Precalculus Examples

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

Step 1

Separate fractions.

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

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

Step 6

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

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

Step 7

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

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

Step 8

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

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

Step 9

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

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

Step 10

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

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Step 10.1

Cancel the common factor.

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

Step 10.2

Rewrite the expression.

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

Step 11

Convert from $\frac{1}{\cos (x)}$ to $\sec (x)$ .

$\sec (x) \csc (x)$