The period of
`f(x)=(1)/(2){(| sinx|)/(cos x)-(|cosx|)/(sinx)}`, is

Options

A. Statement-1 is True, Statement-2 is True, statement-2 is a correct explanation for the statement-1 .
B. Statement-1 is True, Statement-2 is True, statement-2 is not a correct explanation for the statement-1 .
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False , Statement-2 is True.

Explanation

To find the period of the function \( f(x) = \frac{1}{2} \left( \frac{|\sin x|}{\cos x} - \frac{|\cos x|}{\sin x} \right) \), we will analyze the components of the function.

### Step 1: Identify the periods of the components
1. The function \( |\sin x| \) has a period of \( \pi \) because it repeats every \( \pi \) radians.
2. The function \( |\cos x| \) also has a period of \( \pi \) for the same reason.