Verify the identity algebraically. Use the table feature of a graphing utility to check your result numerically. (Simplify at each step.)
\[
\begin{aligned}
\frac{4}{\sin (x)}- & \frac{4}{\csc (x)}=4 \csc (x)-4 \sin (x) \\
\frac{4}{\sin (x)}-\frac{4}{\csc (x)} & =\frac{4 \csc (x)-4 \sin (x)}{(\square)(\csc (x))} \\
& =\frac{4 \csc (x)-4 \sin (x)}{\square} \\
& =4 \csc (x)-4 \sin (x)
\end{aligned}
\]
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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 ：\(\boxed{\text{The given identity } \frac{4}{\sin (x)}- \frac{4}{\csc (x)}=4 \csc (x)-4 \sin (x) \text{ is not correct.}}\)