1. **State the problem:** Simplify the expression $ \frac{\cos x (1 - \sin x)}{\cos x} $. 2. **Recall the formula and rules:** When dividing expressions, common factors in numerator and denominator can be canceled, provided they are not zero. 3. **Simplify the expression:** $$\frac{\cos x (1 - \sin x)}{\cos x}$$ Since $\cos x \neq 0$, we can cancel $\cos x$ in numerator and denominator: $$\frac{\cancel{\cos x} (1 - \sin x)}{\cancel{\cos x}} = 1 - \sin x$$ 4. **Final answer:** $$1 - \sin x$$ This means the original expression simplifies to $1 - \sin x$.