Prove the identity
\(\csc\theta + \cot\theta \equiv \dfrac{1}{\csc\theta - \cot\theta}\)
Solution
\((\csc\theta + \cot\theta)(\csc\theta - \cot\theta) = \csc^2\theta - \cot^2\theta\)
\(= (1 + \cot^2\theta) - \cot^2\theta\)
\(= 1\)
\(\Rightarrow \csc\theta + \cot\theta = \dfrac{1}{\csc\theta - \cot\theta}\)
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