Mathematics - Functions Question with Solution | TestHub

Since $|\sin \mathrm{x}|$ and $\cos \mathrm{x}$ are periodic function with period $\pi$ and $2\pi$ respectively.

Therefore, $\frac{|\sin x|}{\cos x}$ is periodic with period $2\pi$.

Similarly, $\frac{|\cos x|}{\sin x}$ is periodic with period $2\pi$.

So, period of $\mathrm{f}(\mathrm{x})$ is L.C.M. of $\{2\pi ,2\pi \}=2\pi$.