Answer
If $f\left( -x \right)=f\left( x \right)$ , then the function is even; if the function has symmetry about the y-axis, then it will be an even function.
Work Step by Step
We know that even trigonometric functions can be checked by the following steps:
Step I: If $f\left( -x \right)=f\left( x \right)$ , then it will be an even function.
Step II: Graphically, if the function has symmetry about the y-axis, then it will be an even function.
$\begin{align}
& \sin \left( -x \right)=-\sin x \\
& \cos \left( -x \right)=\cos x \\
& \tan \left( -x \right)=-\tan x \\
\end{align}$
Similarly,
$\begin{align}
& \operatorname{cosec}\left( -x \right)=-\operatorname{cosec}x \\
& \sec \left( -x \right)=\sec x \\
& \cot \left( -x \right)=-\cot x \\
\end{align}$
Thus, if any trigonometric function has $f\left( -x \right)=f\left( x \right)$, then it will be an even function, and among six trigonometric functions, $\cos x,\text{ and }\sec x$ are even trigonometric functions.
For example:
$\begin{align}
& \cos \left( -\frac{\pi }{4} \right)=\cos \frac{\pi }{4} \\
& \sec \left( -\frac{\pi }{4} \right)=\sec \frac{\pi }{4} \\
\end{align}$
