The period of the function $f(x)=\sin(\cos\frac{x}{2})+\cos (\sin x)$ 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 $4π$.