1. Establish the identity:
$(\csc θ - \cot θ)^{2} = \frac{1 - \cos θ}{1 + \cos θ}$

Answer

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Answer

$= \frac{(1 - \cos θ) (1 + \cos θ)}{1 - \cos^{2} θ} = \frac{1 - \cos θ}{1 + \cos θ}$

Steps

Step 1 ： $(\csc θ - \cot θ)^{2} = \frac{1}{\sin^{2} θ} - 2 \frac{\cos θ}{\sin^{2} θ} + \frac{\cos^{2} θ}{\sin^{2} θ}$

Step 2 ： $= \frac{1 - 2 \cos θ + \cos^{2} θ}{\sin^{2} θ}$

Step 3 ： $= \frac{(1 - \cos θ) (1 + \cos θ)}{1 - \cos^{2} θ} = \frac{1 - \cos θ}{1 + \cos θ}$