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. \( \frac{\sec (x)}{\tan (x)}=\square \)

To express \( \frac{\sec (x)}{\tan (x)} \) in terms of \( \sin (x) \) and \( \cos (x) \), we use the definitions of secant and tangent: \[ \sec(x) = \frac{1}{\cos(x)} \quad \text{and} \quad \tan(x) = \frac{\sin(x)}{\cos(x)}. \] Now, substituting these into the expression gives: \[ \frac{\sec(x)}{\tan(x)} = \frac{\frac{1}{\cos(x)}}{\frac{\sin(x)}{\cos(x)}}. \] When you divide by a fraction, it’s the same as multiplying by its reciprocal: \[ = \frac{1}{\cos(x)} \cdot \frac{\cos(x)}{\sin(x)}. \] Now, the \( \cos(x) \) terms cancel each other out: \[ = \frac{1}{\sin(x)} = \csc(x). \] Thus, simplified, we have: \[ \frac{\sec(x)}{\tan(x)} = \frac{1}{\sin(x)}. \]