Write the following in terms of \( \sin (x) \) and \( \cos (x) \), and then simplify if possible. Leave your answer in terms of sines and cosines only. \( \cot (x)-\csc (x)=\square \)

To express \( \cot(x) \) and \( \csc(x) \) in terms of \( \sin(x) \) and \( \cos(x) \): 1. The cotangent function is defined as: \[ \cot(x) = \frac{\cos(x)}{\sin(x)} \] 2. The cosecant function is defined as: \[ \csc(x) = \frac{1}{\sin(x)} \] Now substituting these definitions into the expression \( \cot(x) - \csc(x) \): \[ \cot(x) - \csc(x) = \frac{\cos(x)}{\sin(x)} - \frac{1}{\sin(x)} \] Since both terms have a common denominator, we can combine them: \[ = \frac{\cos(x) - 1}{\sin(x)} \] Thus, the final expression is: \[ \cot(x) - \csc(x) = \frac{\cos(x) - 1}{\sin(x)} \]