Question

The period of the function $f\left(x\right)=\frac{\left|\sin x\right|+\left|\cos x\right|}{|\sin x-\cos x|}$ is

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

Answer 1

The correct option is C $\pi$

$f\left(x\right)=\frac{\left|\sin x\right|+\left|\cos x\right|}{|\sin x-\cos x|}$
Period of $|\sin x|+|\cos x|$ is $\frac{\pi }{2}$
Period of $|\sin x-\cos x|$ is $\pi$
L.C.M of $\frac{\pi }{2},\pi$ is $\pi$