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

$\frac{π}{2}$ $\frac{π}{3}$ $\frac{2π}{3}$ $\frac{2π}{5}$

$\frac{π}{2}$

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