Q82 / 200 · Manipal (MET) 2010 · Mathematics

The period of the function $f(x)=|\sin 4 x|+|\cos 4 x|$ is

A
$\pi / 2$
Correct answer
B
$\pi / 8$
C
$\pi / 4$
D
None of these

Solution

Since, $|\sin x|+|\cos x|$ is a periodic function with period $\pi / 2$. $\therefore f(x)=|\sin 4 x|+|\cos 4 x|$ is a periodic function with period $\frac{1}{4} \cdot \frac{\pi}{2} i e, \frac{\pi}{8}$.

Hence, the correct answer is option: 'B'.

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