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$The period of | \sin 3 x | + | \cos 3 x | is$

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$\frac{π}{3}$

$\frac{π}{6}$

$\frac{2 π}{3}$

$π$

answer is C.

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Detailed Solution

$f (x) = |\sin 3 x| + |\cos 3 x|$

$f (x + \frac{π}{6}) = |\sin 3 (x + \frac{π}{6})| + |\cos 3 (x + \frac{π}{6})|$

$f (x + \frac{π}{6}) = |\sin (3 x + \frac{π}{2})| + |\cos (3 x + \frac{π}{2})|$

$f (x + \frac{π}{6}) = |\cos 3 x| + |- \sin 3 x|$

$\Rightarrow f (x + \frac{π}{6}) = |\sin 3 x| + |\cos 3 x| = f (x)$

$∴ period = \frac{π}{6}$

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