Answer
See the verification below.
Work Step by Step
Consider the identity: $\csc x-\cos x\cot x=\sin x$
Solve the left side of the above identity,
$\begin{align}
& \csc x-\cos x\cot x=\frac{1}{\sin x}-\cos x\frac{\cos x}{\sin x} \\
& =\frac{1}{\sin x}-\frac{{{\cos }^{2}}x}{\sin x} \\
& =\frac{1-{{\cos }^{2}}x}{\sin x}
\end{align}$
Now, use the identity $1-{{\cos }^{2}}x={{\sin }^{2}}x$ and solve further,
$\begin{align}
& \csc x-\cos x\cot x=\frac{{{\sin }^{2}}x}{\sin x} \\
& =\sin x
\end{align}$
Now, the right side of the identity $\csc x-\cos x\cot x=\sin x$ is also $\sin x$
Thus, the left side and the right side of the identity $\csc x-\cos x\cot x=\sin x$ are equal.
Hence, the identity $\csc x-\cos x\cot x=\sin x$ is verified.
