Question

The period of $f\left(x\right)=\cos (|\sin x|-|\cos x|)$ is

• A. $\pi$
• B. $2\pi$
• C. $\frac{\pi }{2}$
• D. none of these

Answer 1

The correct option is C $\frac{\pi }{2}$

As, $\cos \theta$ is even and $|\sin x|-|\cos x|$ has the period $\pi$.
$\therefore \cos (|\sin x|-|\cos x|)$ has period $\frac{\pi }{2}$.