But we seek the maximum value. Since \(g(v)\) decreases from near infinity (as \(v \to 1^+\)) to 8 at \(v = 2\), but \(v = 1\) is not included. However, as \(x \to 0^+\) or \(\frac\pi2^-\), one of \(\sin x\) or \(\cos x \to 0\), so \(\sec x\) or \(\csc x \to \infty\), so \(f(x) \to \infty\). - Crosslake