Answer
See the explanation below.
Work Step by Step
We use the trigonometric identity: ${{\csc }^{2}}x=\frac{1}{{{\sin }^{2}}x}$ and $\cot x=\frac{\cos x}{\sin x}$.
Now, the left side can be written as:
$\begin{align}
& \frac{{{\csc }^{2}}x}{\cot x}=\frac{\left( \frac{1}{{{\sin }^{2}}x} \right)}{\left( \frac{\cos x}{\sin x} \right)} \\
& =\frac{1}{{{\sin }^{2}}x}\times \frac{\sin x}{\cos x} \\
& =\frac{1}{\sin x\cos x} \\
& =\frac{2}{2\sin x\cos x}
\end{align}$
Next, we use the trigonometric identities:
$2\sin x\cos x=\sin 2x$ and $\frac{1}{\sin x}=\csc x$
Simplified further,
$\begin{align}
& \frac{2}{2\sin x\cos x}=\frac{2}{\sin 2x} \\
& =2\csc x
\end{align}$
Thus, the left side of the equation is equal to $2\csc x$.
Hence, the left side is equal to $2\csc x$.
