Question

Find the least period of the following function:
| sin x + cos x|

Answer 1

Period of $\sin(x)$ is $2\pi$
Period of $\cos(x)$ is $2\pi$

Adding two functions having $2\pi$ as period produces another function having the same $2\pi$ as a period, so the period of $\sin(x)+\cos(x)$ is also $2\pi$.

$|\sin(x)+\cos(x)|$ flips the negative part over x-axis giving a shorter period : $\boxed{\pi}$