Answer
See the verification below.
Work Step by Step
The left side of the identity is as given below:
$\frac{1}{\sin x\times \cos x}-\frac{\cos x}{\sin x}$
Simplifying the left side gives:
$\begin{align}
& \frac{\sec x}{\sin x}-\frac{\cos x}{\sin x}=\frac{\sec x-\cos x}{\sin x} \\
& =\frac{\frac{1}{\cos x}-\cos x}{\sin x} \\
& =\frac{1-{{\cos }^{2}}x}{\sin x\times \cos x}
\end{align}$
Simplifying further,
$\begin{align}
& \frac{1-{{\cos }^{2}}x}{\sin x\times \cos x}=\frac{{{\sin }^{2}}x}{\sin x\times \cos x} \\
& =\frac{\sin x}{\cos x} \\
& =\tan x
\end{align}$
Since, $\text{left side = right side}$ , we can say that the given identity is true.
Thus, it is verified.
