Question

The period of the function $f\left(x\right)=\sin \left(\cos \frac{x}{2}\right)+\cos \left(\sin x\right)$ is

• A. $\frac{\pi }{2}$
• B. $2\pi$
• C. $\pi$
• D. $4\pi$

Answer 1

The correct option is D $4\pi$

Given $f\left(x\right)=\sin \left(\cos \frac{x}{2}\right)+\cos \left(\sin x\right)$

Period of $\cos \frac{x}{2}$ is $4\pi$ and period of $\sin x$ is $2\pi$

$\therefore$ period of $f\left(x\right)$ is L.C.M. of $4\pi$ and $2\pi$ which is equal to $4\pi$