Discussion
The expression \((\csc \theta - \cot \theta)^2\) is equal to:
Answer: B
Convert to sines and cosines:
\((\frac{1}{\sin \theta} - \frac{\cos \theta}{\sin \theta})^2 = (\frac{1 - \cos \theta}{\sin \theta})^2 = \frac{(1 - \cos \theta)^2}{\sin^2 \theta}\).
Using the identity \(\sin^2 \theta = 1 - \cos^2 \theta = (1 - \cos \theta)(1 + \cos \theta)\), the expression becomes:
\(\frac{(1 - \cos \theta)^2}{(1 - \cos \theta)(1 + \cos \theta)} = \frac{1-\cos \theta}{1+\cos \theta}\).
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