The period of the function $f(x)=\frac{|\sin x|+|\cos x|}{|\sin x-\cos x|}$ is

$\frac{π}{4}$ $2π$ $\frac{π}{2}$ $π$

$π$

Since period of $|\sin x | + |\cos x|$ is $\frac{π}{2}$ and period of $|\sin x – \cos x|$ is $π$ so period of $\frac{|\sin x|+|\cos x|}{|\sin x-\cos x|}$ is $π$