Question

$f(x)=|\sin \,2x|+|\cos \,2x|$ is a periodic function with period

• A. $\pi$
• B. $\frac{\pi }{2}$
• C. $\frac{\pi }{4}$
• D. $\frac{\pi }{8}$

Answer 1

Answer: (C)

$f(x)=|\sin \,2x|+|\cos \,2x|$ Since, $|\sin x|+|\cos x|$
is a periodic function with period
$\pi /2.$
$\therefore$ $|\sin \,2x|+\cos \,2x|$
has period $=\frac{1}{2}.\frac{\pi }{2}=\frac{\pi }{4}$