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Answer 1

Answer:

$\huge { \green{ {\boxed{Solution}}}}$

$\implies \dfrac{cosec \: \theta}{cosec \:\theta - 1 } + \dfrac{cosec \: \theta}{cosec \: \theta + 1}$

$\implies \dfrac{cosec \: \theta \: (cosec \:\theta + 1) + cosec \: \theta \: (cosec \:\theta - 1)}{ {cosec \: \theta}^{2} - 1 }$

$\implies\dfrac{{cosec \: }^{2} \theta + cosec \: \theta \: + {cosec \: }^{2} \theta - cosec \: \theta \: }{ {cosec \: }^{2} \theta \: - 1}$

$\implies \dfrac{ 2 \: {cosec}^{2} \theta \: }{{cosec \: }^{2} \theta - 1}$

after this proceed by taking cosec^2 - 1 = cot^2