1. **State the problem:** Simplify the expression $$\frac{\cos(\theta)}{1 - \sin(\theta)} - \tan(\theta)$$. 2. **Rewrite the tangent in terms of sine and cosine:** $$\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$$. 3. **Rewrite the original expression:** $$\frac{\cos(\theta)}{1 - \sin(\theta)} - \frac{\sin(\theta)}{\cos(\theta)}$$. 4. **Find a common denominator:** The common denominator is $$(1 - \sin(\theta)) \cos(\theta)$$. 5. **Rewrite each term over the common denominator:** $$\frac{\cos^2(\theta)}{(1 - \sin(\theta))\cos(\theta)} - \frac{\sin(\theta)(1 - \sin(\theta))}{(1 - \sin(\theta))\cos(\theta)}$$. 6. **Combine the terms:** $$\frac{\cos^2(\theta) - \sin(\theta)(1 - \sin(\theta))}{(1 - \sin(\theta))\cos(\theta)}$$. 7. **Expand the numerator:** $$\cos^2(\theta) - \sin(\theta) + \sin^2(\theta)$$. 8. **Recall the Pythagorean identity:** $$\sin^2(\theta) + \cos^2(\theta) = 1$$. 9. **Substitute and simplify numerator:** $$1 - \sin(\theta)$$. 10. **Now the expression is:** $$\frac{1 - \sin(\theta)}{(1 - \sin(\theta))\cos(\theta)}$$. 11. **Cancel common terms in numerator and denominator:** $$\frac{1}{\cos(\theta)}$$. 12. **Final simplified expression:** $$\sec(\theta)$$. **Answer:** $$\sec(\theta)$$.