Answer
\[\begin{gathered}
we\,obtained\,zero\,in\,denominator\,,\,\ so\, the\, expression\, \hfill \\
is\,undefined. \hfill \\
\end{gathered} \]
Work Step by Step
\[\begin{gathered}
Using\,\,definition\,.{\text{ of }}\,\,\sec x \hfill \\
\hfill \\
\sec \,\,\left( {\frac{{5\pi }}{2}} \right) = \frac{1}{{\cos \,\left( {\frac{{5\pi }}{2}} \right)}} \hfill \\
\hfill \\
the\,\,period\,of\,cosine\,function\,is\,2\pi \, \hfill \\
\hfill \\
\frac{1}{{\cos \,\left( {\frac{{5\pi }}{2}} \right)}} = \frac{1}{{\cos \,\,\left( {\frac{{5\pi }}{2} - 2\pi } \right)}} = \frac{1}{{\cos \,\left( {\frac{\pi }{2}} \right)}} = \frac{1}{0} \hfill \\
\hfill \\
since\,\,we\,obtained\,zero\,in\,denominator\,,\,\exp ression\, \hfill \\
is\,undefined. \hfill \\
\hfill \\
\end{gathered} \]
