Step 1 :Define x as a symbol, then define the left and right sides of the equation as \(\frac{4}{\sin (x)}- \frac{4}{\csc (x)}\) and \(4 \csc (x)-4 \sin (x)\) respectively.
Step 2 :Simplify both sides of the equation. The simplified left side is \(-4\sin(x) + \frac{4}{\sin(x)}\) and the simplified right side is \(0\).
Step 3 :Check if both sides are equal. The result is False.
Step 4 :The simplified left side of the equation is not equal to the simplified right side of the equation.
Step 5 :\(\boxed{\text{The given identity } \frac{4}{\sin (x)}- \frac{4}{\csc (x)}=4 \csc (x)-4 \sin (x) \text{ is not correct.}}\)