[tex]\cos(x)[/tex] is an even function, while [tex]\sin(x)[/tex] is odd. This means
[tex]\cos(-x) = \cos(x) \text{ and } \sin(-x) = -\sin(x)[/tex]
[tex]\cot(x)[/tex] is defined by
[tex]\cot(x) = \dfrac{\cos(x)}{\sin(x)}[/tex]
so it is an odd function, since
[tex]\cot(-x) = \dfrac{\cos(-x)}{\sin(-x)} = \dfrac{\cos(x)}{-\sin(x)} = -\cot(x)[/tex]
Putting everything together, it follows that
[tex]\cot(-x) \cos(-x) \sin(-x) = (-\cot(x)) \cos(x) (-\sin(x)) \\\\~~~~~~~~= \cot(x) \cos(x) \sin(x) \\\\ ~~~~~~~~= \cos^2(x)[/tex]
