Question

The period of the function $f\left(x\right)=\frac{|\sin x|-|\cos x|}{|\sin x\cos x|}$ is

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

Answer 1

The correct option is C $\pi$

$f\left(x\right)=\frac{\left|\sin x\right|-\left|\cos x\right|}{\left|\sin x\cos x\right|}$
$=\frac{\left|\sin x\right|-\left|\cos x\right|}{\left|\frac{1}{2}2\sin x\cos x\right|}=\frac{\left|\sin x\right|-\left|\cos x\right|}{\left|\frac{1}{2}\sin 2x\right|}$
As period of $\left|\sin x\right|,\left|\cos x\right|$ is $\pi ,$ and period of $\left|\sin 2x\right|$ is $\frac{\pi }{2}$.
Therefore period of $f\left(x\right)$ is $\pi$