Find the period of the following functions f(x) = |sin x| + |cos x|

$f(x) = |\sin x| + |\cos x|$

Period of both $|\sin x|$ and $|\cos x|$ is π.

So, we can consider period of f(x) to be π.

But $f(\frac{π}{2}+x)=\left|\sin(\frac{π}{2}+x)\right|+\left|\cos(\frac{π}{2}+x)\right|$

$= |\cos x| + |-\sin x|$

$= |\cos x| +| \sin x|$

= f(x)

So, period of f(x) is π/2.