Verify that the equation is an idently $\csc x-\sin x=\cos x \cot x$ To verify the identity, start with the more complicated side and transform it to look like the other side. Choose the \[ \begin{aligned} \csc x-\sin x & =\square-\sin x \\ & =\square \\ & =\square \\ & =\square \\ & =\cos x \cot x \end{aligned} \] Use a common denominator to perform the subtraction. Separate the expression into two factors.

Step 1 ：Start with the more complicated side of the equation, which is \(\csc x - \sin x\).

Step 2 ：Convert \(\csc x\) to \(\frac{1}{\sin x}\), as \(\csc x\) is the reciprocal of \(\sin x\).

Step 3 ：Perform the subtraction by finding a common denominator, which gives \(-\sin^2 x + 1\).

Step 4 ：Simplify the expression to \(\frac{\cos^2 x}{\sin x}\).

Step 5 ：Compare the simplified expression to the other side of the equation, which is \(\cos x \cot x\).

Step 6 ：Convert \(\cot x\) to \(\frac{\cos x}{\sin x}\), which gives \(\frac{\cos^2 x}{\sin x}\).

Step 7 ：The simplified left side of the equation is equal to the simplified right side of the equation.

Step 8 ：\(\boxed{\text{Therefore, the equation } \csc x-\sin x=\cos x \cot x \text{ is an identity.}}\)