Answer
$\csc{(-x)} = -\csc{x}$.
Please refer to the step-by-step part for the complete solution.
Work Step by Step
RECALL:
(1) The sine function is an odd function, which means $\sin{(-x)} = -\sin{x}$ for all numbers in its domain.
(2) $\csc{x} = \dfrac{1}{\sin{x}}$
Therefore,
$\csc{(-x)}
\\=\dfrac{1}{\sin{(-x)}}
\\=\dfrac{1}{-\sin{x}}
\\=-\dfrac{1}{\sin{x}}
\\=-\csc{x}$
Thus,
$\csc{(-x)} = -\csc{x}$