To find the stationary point, we need to find the derivative of \(y = \frac{e^x}{\cos x}\) and set it to zero.

Using the quotient rule, the derivative is:

\(\frac{d}{dx} \left( \frac{e^x}{\cos x} \right) = \frac{e^x \cos x + e^x \sin x}{\cos^2 x}\)

Set the derivative to zero:

\(e^x \cos x + e^x \sin x = 0\)

Factor out \(e^x\):

\(e^x (\cos x + \sin x) = 0\)

Since \(e^x \neq 0\), we have:

\(\cos x + \sin x = 0\)

This simplifies to:

\(\tan x = -1\)

The solution for \(x\) in the interval \(-\frac{1}{2}\pi < x < \frac{1}{2}\pi\) is:

\(x = -\frac{1}{4}\pi\)