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

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

ManipalManipal 2010

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, $\frac{\pi}{8}$.