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

$\frac{π}{2}$ $2π$ $π$ $4π$

$4π$

If periodic then $f (x +T)= f (x)$ Put x = 0 $⇒ f (T)= f (0) ⇒ \sin(\frac{\cos T}{2}) +\cos(\sin T)=\sin(1)+ \cos(0)$ Smallest positive value of T satisfying this equation is $4π$. Hence period of f(x) is $4π$.