Question 837620
*[tex \large \frac{\cos \theta \cot \theta}{1 - \sin \theta} - 1 = \frac{ \frac{\cos^2 \theta}{\sin \theta}}{1 - \sin \theta} - 1]


*[tex \large = \frac{\cos^2 \theta}{\sin \theta (1 - \sin \theta} - 1]


*[tex \large = \frac{1 - \sin^2 \theta}{\sin \theta (1 - \sin \theta)} - 1]


*[tex \large = \frac{(1 - \sin \theta)(1 + \sin \theta)}{\sin \theta (1 - \sin \theta)} - 1]


*[tex \large = \frac{1 + \sin \theta}{\sin \theta} - 1]


*[tex \large = 1 + \csc \theta - 1]


*[tex \large = \csc \theta]