Question

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

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

Answer 1

Answer: (D)

$4\pi$

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

$f(4\pi +x)=sin\left(cos\right(2\pi +\frac{x}{2}\left)\right)+cos\left(sin\right(4\pi +x\left)\right)$

$f(4\pi +x)=sin\left(cos\frac{x}{2}\right)+cos\left(sinx\right)$

$f\left(x\right)=f(4\pi +x)$

Hence, period of f(x) is $4\pi$