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Q.

The period of $|\sin x| + |\cos x|$ is

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a

$π$

b

$\frac{π}{4}$

c

$2 π$

d

$\frac{π}{2}$

answer is D.

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Detailed Solution

$f (x) = |s i n x| + |\cos x|$
$f (π + x) = |s i n (π + x)| + |\cos (π + x)|$
$= |- s i n x| + |- \cos x|$
$= |s i n x| + |\cos x| = f (x)$
$f (\frac{π}{2} + x) = |s i n (\frac{π}{2} + x)| + |\cos (\frac{π}{2} + x)|$
$= | \cos x | + | - \sin x | = | \cos x | + | \sin x | = f (x)$

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