Question

The period of the function $|sinx|+|cosx|$ is

• A. $\frac{\pi }{2}$
• B. $2\pi$
• C. $4\pi$
• D. $\pi$

Answer 1

The correct option is A $\frac{\pi }{2}$

The smallest of $\frac{\pi }{2},2\pi ,4\pi ,\pi$ is $\frac{\pi }{2}$
Let $f\left(x\right)=|sinx|+|cosx|.$
$\therefore f(x+\frac{\pi }{2})=\left|sin(x+\frac{\pi }{2})\right|+\left|cos(x+\frac{\pi }{2})\right|$
$=|cosx|+|-sinx|$
$=|cosx|+|sinx|$
=f (x)
$\therefore$ The period of given function is $\frac{\pi }{2}$