Precalculus Examples

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

Step 1

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

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

Step 2

Multiply the numerator by the reciprocal of the denominator.

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

Step 3

Multiply $\frac{\sin (x)}{\cos (x)}$ by $\frac{1}{1 - \cos (x)}$ .

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

Step 4

Separate fractions.

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

Step 5

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

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

Step 6

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

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