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  4. The function f(x) = |sin 4x |+|cos 2x|, is a periodic function with period :

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

JEE MainJEE Main 2014Trigonometric Functions

Solution:

$| sin\,x | + | cos\,x |$ is periodic with period $\frac{\pi}{2}$.
Hence, $f\left(x\right) = |sin \,4x| + |cos \,2x|$
is also periodic function with period $\frac{\pi }{2}$