Function fleft( x right) = left| {sin ,4x} right| + left| {cos ,2x} right| , is a periodic function

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1.Relation and Function

hard

The function $f\left( x \right) = \left| {\sin \,4x} \right| + \left| {\cos \,2x} \right|$, is a periodic function with period

A

$2 \pi $

B

$\pi $

C

$\frac{\pi}{2}$

D

$\frac{\pi}{4}$

(JEE MAIN-2014)

Solution

$\left| {\sin \,x} \right| + \left| {\cos \,x} \right|$ is periodic with oeriod $\frac{\pi }{2}$.

Hence, $f\left( x \right) = \left| {\sin \,4x} \right| + \left| {\cos 2\,x} \right|$

is also periodic function with period $\frac{\pi }{2}$

Standard 12

Mathematics

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