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Standard XII

Mathematics

Composite Function

The period of...

Question

The period of $f (x) = cos (cos x) + cos (sin x)$ , is

\frac{π}{2}

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\frac{π}{1}

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\frac{π}{4}

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2 π

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Solution

The correct option is A $\frac{π}{2}$
Here, $cos (cos x)$ has period $π$ ; as it is even,
Also $cos (sin x)$ has period $π$ as it is even.
Thus, period of $f (x) = \frac{1}{2}$ (LCM of $π$ and $π)$
Hence, period of $f (x) = \frac{π}{2}$

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The period of f(x)=cos(cosx)+cos(sinx), is

The correct option is A π2Here, cos(cosx) has period π; as it is even, Also cos(sinx) has period π as it is even.Thus, period of f(x)=12(LCM of π and π)Hence, period of f(x)=π2

The period of $f (x) = cos (cos x) + cos (sin x)$ , is

The correct option is A $\frac{π}{2}$
Here, $cos (cos x)$ has period $π$ ; as it is even,
Also $cos (sin x)$ has period $π$ as it is even.
Thus, period of $f (x) = \frac{1}{2}$ (LCM of $π$ and $π)$
Hence, period of $f (x) = \frac{π}{2}$