Answer
See the full explanation below.
Work Step by Step
By solving the left side of the identity, we get:
$\cot x+\tan x=\left( \csc x \right)\left( \sec x \right)$:
$\begin{align}
& \cot x+\tan x=\frac{\cos x}{\sin x}+\frac{\sin x}{\cos x} \\
& =\frac{{{\cos }^{2}}x+{{\sin }^{2}}x}{\sin x\cos x} \\
& =\frac{1}{\sin x\cos x} \\
& =\frac{1}{\sin x}\times \frac{1}{\cos x}
\end{align}$
Therefore,
$\cot x+\tan x=\left( \csc x \right)\left( \sec x \right)$
Thus, the solution is that the identity is correct.
