We minimize this expression for $ s \in (\sqrt2, \sqrt2] $, since $ \sin x + \cos x = \sqrt2 \sin\left(x + \frac\pi4\right) $, and maximum is $ \sqrt2 $. Wait — maximum is $ \sqrt2 $, minimum is 1 (approaching at endpoints), but in the open interval $ (0, \frac\pi2) $, $ s \in (1, \sqrt2) $. - Groen Casting