Which of the following functions has period $\mathrm{\pi }$?

$$\begin{gathered} \text{ Period of }2\cos \left(\frac{2\mathrm{\pi x}}{3}\right)+3\sin \left(\frac{\mathrm{\pi x}}{3}\right) \\ =\text{ L.C.M. }\left(\frac{2\mathrm{\pi }}{2\mathrm{\pi }/3},\frac{2\mathrm{\pi }}{\mathrm{\pi }/3}\right)=6 \\ \text{ Period of }4\cos \left(2\mathrm{\pi x}+\frac{\mathrm{\pi }}{2}\right)+2\sin \left(\mathrm{\pi x}+\frac{\mathrm{\pi }}{4}\right) \\ =\text{ L.C.M. }\left(\frac{2\mathrm{\pi }}{2\mathrm{\pi }},\frac{2\mathrm{\pi }}{\mathrm{\pi }}\right)=2 \\ \text{ Period of }|\tan \mathrm{x}|+\cos 2\mathrm{x}=\text{ L.C.M. }\left(\mathrm{\pi },\frac{2\mathrm{\pi }}{2}\right)=\mathrm{\pi } \end{gathered}$$