Find the period of
(a) $[sin 3 x] + [cos 6 x]$

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Solution

The period of $[sin 3 x] = \frac{2 π}{3}$
and period of $[cos 6 x] = \frac{π}{6}$
$∴$ period of $[sin 3 x] + [cos 6 x]$
$=$ L.C.M of $\frac{2 π}{3}$ and $\frac{π}{6}$
$= \frac{L . C . M (2 π, π)}{H . C . F (3, 6)} = \frac{2 π}{3}$

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