Question

The period of the function $f\left(x\right)=\sin \left(\cos x\right)+\cos \left(\sin x\right)$ equal

• A. $8\pi$
• B. $4\pi$
• C. $\pi$
• D. $2\pi$

Answer 1

Answer: (D)

$2\pi$

Consider the given function $\sin \left(\cos x\right)+\cos \left(\sin x\right)$

We know that period of sinx and cos x is $2\pi$

The period of a function of type $f\left(g\left(x\right)\right)$ (composite function )is the same as the

Period of the $g\left(x\right)$

And the period of a function $h\left(x\right)=f\left(x\right)+g\left(x\right)$ is the LCM of the periodic function $f\left(x\right)$and$g\left(x\right)$

So,

Applying the above two, perod is LCM of $2\pi ,2\pi$ which is $2\pi$.