Find period of the following function Find period of : 
$$f(x)=| \sin(x) + \cos(x) |$$
Attempt:
Let $$f(x)=|\sin x +\cos x|\tag{I}$$
Let $t$ be the required period,
So,
$f(x)=f(x+t)$  
Putting $x=0$ we get,
$f(0)=f(t)$
f(0)=1 (from 'I')
Now we have the following,
$1=| \sin t + \cos t |$
If we put $t=\pi/2$ ,that would satisfy the equation. But when I put $t=\pi/2$ in $f(x+t)$,
I do not get $f(x)$ ,that means $\pi/2$ is not the period of the function. What I have done wrong?

Another approach: $\mid \sin x + \cos x\mid$ will have the same period as $(\sin x + \cos x)^2 = 1 + \sin{2x}$. Period of $\sin{2x} = 2\pi/2 = \pi$
