#### Answer

The Domain is
$x \ne \frac{\pi}{2}+2n\pi $, (n any integer)

#### Work Step by Step

$f(x) = \frac{cos (x)}{1-sin(x)}$
Lets find the Domain:
$1 - sin (x) \ne 0$
$sin (x) \ne 1$
$x \ne \frac{\pi}{2}+2n\pi $, (n any integer)
The Domain is
$x \ne \frac{\pi}{2}+2n\pi $, (n any integer)