The period of the function $f(x)=\sin\left(\cos\frac{x}{2}\right)+\cos(\sin x)$ is equal to
Answer & explanation
Correct answer: option 4
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 $4π$.