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

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

J & K CETJ & K CET 2011Trigonometric Functions

Solution:

$ 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} $