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Thus, \((\sec x + \csc x)^2\) is unbounded on \(0 < x < \frac{\pi}{2}\), and has no maximum.
But wait — is that correct?
Let \(x \to 0^+\), \(\sec x \to 1\), \(\csc x \to \infty\), so sum \(\to \infty\). Similarly near \(\frac{\pi}{2}^-\). So the expression goes to infinity.

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