1. **State the problem:** Simplify the function $$f(x) = \frac{1 - \sin^2(x)}{\cos(x)}$$. 2. **Recall the Pythagorean identity:** $$\sin^2(x) + \cos^2(x) = 1$$, which implies $$1 - \sin^2(x) = \cos^2(x)$$. 3. **Substitute the identity into the function:** $$f(x) = \frac{\cos^2(x)}{\cos(x)}$$ 4. **Simplify the fraction by canceling one $$\cos(x)$$ term:** $$f(x) = \frac{\cancel{\cos(x)} \cdot \cos(x)}{\cancel{\cos(x)}}$$ 5. **Result after cancellation:** $$f(x) = \cos(x)$$ 6. **Important note:** The simplification is valid only where $$\cos(x) \neq 0$$ because division by zero is undefined. **Final answer:** $$f(x) = \cos(x), \quad \text{for } \cos(x) \neq 0$$