The expression of $$\frac{\cot \theta + \cosec \theta - 1}{\cot \theta + \cosec \theta + 1}$$ is equal to

A

$$\frac{1 + \cos \theta}{\sin \theta}$$

B

$$\frac{1 - \cos \theta}{\sin \theta}$$

C

$$\frac{\cot \theta + 1}{\cosec \theta}$$

D

$$\frac{\cot \theta - 1}{\cosec \theta}$$