1. State the problem: Simplify the expression $$\frac{\cos(\theta)}{1 - \sin(\theta)} - \tan(\theta)$$. 2. Recall that $$\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$$. 3. Rewrite the expression using this identity: $$\frac{\cos(\theta)}{1 - \sin(\theta)} - \frac{\sin(\theta)}{\cos(\theta)}$$ 4. To combine the terms, find the common denominator $$\cos(\theta)(1 - \sin(\theta))$$: $$\frac{\cos^2(\theta)}{\cos(\theta)(1 - \sin(\theta))} - \frac{\sin(\theta)(1 - \sin(\theta))}{\cos(\theta)(1 - \sin(\theta))}$$ 5. Combine the numerators: $$\frac{\cos^2(\theta) - \sin(\theta)(1 - \sin(\theta))}{\cos(\theta)(1 - \sin(\theta))}$$ 6. Expand the numerator: $$\cos^2(\theta) - \sin(\theta) + \sin^2(\theta)$$ 7. Use the Pythagorean identity $$\sin^2(\theta) + \cos^2(\theta) = 1$$ to simplify the numerator: $$1 - \sin(\theta)$$ 8. Now the expression is: $$\frac{1 - \sin(\theta)}{\cos(\theta)(1 - \sin(\theta))}$$ 9. Cancel the common term $$1 - \sin(\theta)$$ (assuming $$\theta$$ is such that $$1 - \sin(\theta) \neq 0$$): $$\frac{1}{\cos(\theta)}$$ 10. Therefore, the simplified form is $$\sec(\theta)$$, since $$\sec(\theta) = \frac{1}{\cos(\theta)}$$. Final answer: $$\boxed{\sec(\theta)}$$