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