Answer
Verified below.
Work Step by Step
We have $\tan x+\frac{1}{\tan x}=\frac{1}{\sin x\cos x}$
By evaluating the left side,
$\begin{align}
& \text{Left side}=\tan x+\frac{1}{\tan x} \\
& =\frac{{{\tan }^{2}}x+1}{\tan x} \\
& =\frac{{{\sec }^{2}}x}{\tan x} \\
& =\frac{{}^{1}/{}_{{{\cos }^{2}}x}}{{\sin x}/{\cos x}\;}
\end{align}$
$=\frac{1}{\sin x\cos x}$
Thus, $\text{left side = right side}$. So, we can say that the identity is true. Hence, verified.
