The fundamental period of the function $f (x) = {sin}^{3} x + {cos}^{2} x$ is

π

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2 π

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\frac{2 π}{3}

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\frac{π}{3}

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Solution

The correct option is B $2 π$
We have,
$f (x) = {sin}^{3} x + {cos}^{2} x = \frac{3 sin x - sin 3 x}{4} + {cos}^{2} x$
$= \frac{3}{4} sin x - \frac{3}{4} sin 3 x + {cos}^{2} x$

So, period of $f (x) = L . C . M (2 π, \frac{2 π}{3}, π) = \frac{L . C . M of (2 π, 2 π, π)}{H . C . F of (1, 3, 1)} = 2 π$

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