Precalculus Examples

$\frac{4 \sin (x) \sec (x)}{\tan (x)}$

Step 1

Separate fractions.

$\frac{4 \sec (x)}{1} \cdot \frac{\sin (x)}{\tan (x)}$

Step 2

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

$\frac{4 \sec (x)}{1} \cdot \frac{\sin (x)}{\frac{\sin (x)}{\cos (x)}}$

Step 3

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

$\frac{4 \sec (x)}{1} (\sin (x) \frac{\cos (x)}{\sin (x)})$

Step 4

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

$\frac{4 \sec (x)}{1} (\frac{\sin (x)}{1} \cdot \frac{\cos (x)}{\sin (x)})$

Step 5

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

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Step 5.1

Cancel the common factor.

$\frac{4 \sec (x)}{1} (\frac{\sin (x)}{1} \cdot \frac{\cos (x)}{\sin (x)})$

Step 5.2

Rewrite the expression.

$\frac{4 \sec (x)}{1} \cos (x)$

Step 6

Divide $4 \sec (x)$ by $1$ .

$4 \sec (x) \cos (x)$

Step 7

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

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Step 7.1

Add parentheses.

$4 (\sec (x) \cos (x))$

Step 7.2

Rewrite $4 \sec (x) \cos (x)$ in terms of sines and cosines.

$4 (\frac{1}{\cos (x)} \cos (x))$

Step 7.3

Cancel the common factors.

$4 \cdot 1$

Step 8

Multiply $4$ by $1$ .

$4$