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

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

KEAMKEAM 2006

Solution:

$ |\sin x| $ and $ |\cos x| $ are periodic functions with period $ \pi $ . $ \therefore $ $ |\sin x|+|\cos x| $ is periodic with period is the LCM Of $ (\pi ,\pi )=\pi $ $ \therefore $ Period of $ |\sin x|+|\cos x|=\pi $ .