Simplify. \( \frac{\cot (-x) \sin (-x)}{\cos x} \) \( [?] \)

To simplify \( \frac{\cot (-x) \sin (-x)}{\cos x} \), we start by using the properties of the cotangent and sine functions. Recall that: - \( \cot(-x) = -\cot(x) \) (the cotangent function is odd) - \( \sin(-x) = -\sin(x) \) (the sine function is also odd) Now substituting these properties into the expression gives: \[ \frac{\cot(-x) \sin(-x)}{\cos x} = \frac{-\cot(x) \cdot (-\sin(x))}{\cos x} = \frac{\cot(x) \sin(x)}{\cos x} \] Now we know \( \cot(x) = \frac{\cos(x)}{\sin(x)} \), so we can rewrite the expression: \[ \frac{\cot(x) \sin(x)}{\cos x} = \frac{\frac{\cos(x)}{\sin(x)} \sin(x)}{\cos x} \] The \( \sin(x) \) in the numerator and denominator cancels out: \[ = \frac{\cos(x)}{\cos x} = 1 \] Thus, the simplified expression is: \[ \boxed{1} \]