$f(x)=\frac{\cos x}{\left[\frac{2 x}{\pi}\right]+\frac{1}{2}}$, where x is not an integral multiple of $\pi$ and [.] denotes the greatest integer function, is

• Correct answer
  A

  an odd function
• B

  an even function
• C

  neither odd nor even
• D

  None of these

Solution

$=-\frac{\cos x}{\left[\frac{2 x}{\pi}\right]+\frac{1}{2}}=-f(x)$ Therefore, $f(x)$ is an odd function.

Hence, the correct answer is option: 'A'.