You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Composite Function

The period of...

Question

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

\frac{π}{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{π}{1}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{π}{4}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 π

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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 $f (x) = \frac{π}{2}$

Suggest Corrections

Similar questions

Q. Assertion :The least period of

f (x) = cos (sin x) + cos (cos x) + sin 4 x

is equal to

π

Reason: If

f (x + π) = f (x)

then

π

is the period of

f (x)

Q. Assertion (A) : The least period of the function, f(x)

= cos (cos x)

+ cos (sin x) + sin 4 x

π

Reason (R) : since

f (x +

π

) = f (x)

Q. The minimum & maximum value of

f (x) = sin (cos x) + cos (sin x) \forall - \frac{π}{2} \leq x \leq \frac{π}{2}

are respective

Q. If

f (x) = sin x, \forall x \in [0, \frac{π}{2}],

f (x) + f (π - x) = 2, \forall x \in (\frac{π}{2}, π]

and

f (x) = f (2 π - x), \forall x \in (π, 2 π],

then the area enclosed by

y = f (x)

and the

x

-axis is

Let $f (x) = {\begin{matrix} - π, if & - π < x \leq 0 π, if & 0 < x \leq π \end{matrix}$
be a periodic function of period $2 π$ . The coefficient of $sin 5 x$ in the Fourier series expansion of f(x) in the interval $[- π, π]$ is

Join BYJU'S Learning Program

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 $f (x) = \frac{π}{2}$