Let S be the set of all point in ($-\mathrm{\pi },\mathrm{\pi }$ ,)  at which the function f(x) = min {sinx, cosx} is not differentiable

$\mathrm{f}\left(\mathrm{x}\right)=\min \{\sin \mathrm{x}, \cos \mathrm{x}\}, \mathrm{x}\in \left(-\mathrm{\pi },\mathrm{\pi }\right)$

$$\begin{gathered} \mathrm{f}\left(\mathrm{x}\right)=\left\{\begin{array}{ll}\cos \mathrm{x}& -\mathrm{\pi }<\mathrm{x}<-\frac{3\mathrm{\pi }}{4}\\ \sin \mathrm{x}& -\frac{2\mathrm{\pi }}{4}<\mathrm{x}<\frac{\mathrm{\pi }}{4}\\ \cos \mathrm{x}& \frac{\mathrm{\pi }}{4}<\mathrm{x}<\mathrm{\pi }\end{array}\right. \\ \Rightarrow \mathrm{f}\left(\mathrm{x}\right) \mathrm{is} \mathrm{not} \mathrm{differentiable} \mathrm{at} \mathrm{x}=\frac{-3\mathrm{\pi }}{4}, \frac{\mathrm{\pi }}{4} \\ \mathrm{s}=\left\{\frac{-3\mathrm{\pi }}{4}, \frac{\mathrm{\pi }}{4}\right\} \\ \mathrm{s}\le \left\{\frac{-3\mathrm{\pi }}{4}, \frac{-\mathrm{\pi }}{4},\frac{\mathrm{\pi }}{4}, \frac{3\mathrm{\pi }}{4}\right\} \end{gathered}$$