Problem
1. Establish the identity: \[ (\csc \theta-\cot \theta)^{2}=\frac{1-\cos \theta}{1+\cos \theta} \]
Solution
Step 1 ：\( (\csc \theta - \cot \theta)^{2} = \cfrac{1}{\sin^{2}\theta} - 2\cfrac{\cos\theta}{\sin^{2}\theta} + \cfrac{\cos^{2}\theta}{\sin^{2}\theta} \)
Step 2 ： \( = \cfrac{1 - 2\cos\theta + \cos^2\theta}{\sin^{2}\theta} \)
Step 3 ： \( = \cfrac{(1 - \cos\theta)(1 + \cos\theta)}{1 -\cos^2\theta} = \cfrac{1 - \cos\theta}{1 + \cos\theta} \)
