Simplify -cot(x)sin(x)

$- \cot (x) \sin (x)$

Add parentheses.

$- (\cot (x) \sin (x))$

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

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

Cancel the common factors.

$- \cos (x)$