The period of the function $f(x)=\sin(\c

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

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

Options:

$\frac{π}{2}$

$2π$

$π$

$4π$

Correct Answer:

$4π$

Explanation:

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 $4π$.