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. \( \cot (x)-\csc (x)= \)

To express \( \cot(x) - \csc(x) \) in terms of \( \sin(x) \) and \( \cos(x) \), we start with the definitions of cotangent and cosecant: \[ \cot(x) = \frac{\cos(x)}{\sin(x)} \quad \text{and} \quad \csc(x) = \frac{1}{\sin(x)} \] Now substituting these definitions into the expression, we have: \[ \cot(x) - \csc(x) = \frac{\cos(x)}{\sin(x)} - \frac{1}{\sin(x)} \] Now, we can combine the two fractions: \[ \cot(x) - \csc(x) = \frac{\cos(x) - 1}{\sin(x)} \] This expression is now in terms of sine and cosine. There are no further simplifications possible, so the final answer is: \[ \frac{\cos(x) - 1}{\sin(x)} \]