The period of the function $f\left(x\right)=\left|\cos \frac{x}{2}\right|+|\sin x|$ is $\mathrm{k\pi }$, then k is equal to

We know that $\left| \sin x\right|$ and $\left|\cos x \right|$ are periodic
functions each with period $\mathrm{\pi }$. Therefore, $\left|\cos \frac{x}{2}\right|$ is periodic with period 2$\mathrm{\pi }$ 

Thus, $f\left(x\right)=\left|\cos \frac{x}{2}\right|+|\sin x|$ is periodic with period 2$\mathrm{\pi }$ 

$\therefore k\pi =2\pi \Rightarrow k=2.$