Question

The period of the function $f\left(x\right)=|sinx|+|cosx|$ is

• A. $\pi /2$
• B. $\pi$
• C. $2\pi$
• D. $\pi /4$

Answer 1

The correct option is A $\pi /2$

$\text{Given,}$

$f\left(x\right)=1\sin x|+|\cos x\mid$

$\because \text{period}|\sin x|=\pi$

and peried $\mid \cos x=\pi$

But , we should alio check. $(\frac{\pi }{2}-x)$

$f(\frac{\pi }{2}-x)=\left|\sin (\frac{\pi }{2}-x)\right|+\mid \cos (\frac{\pi }{2}-x)$

$f(\frac{\pi }{2}-x)$=$|\cos x|+|\sin x|$4

$\text{Here,}f(\frac{\pi }{2}-x)=f\left(x\right)$

$\text{:. The period is}\frac{\pi }{2}$

$\text{option}A=\frac{\pi }{2}$