Question

cos square theta / sin theta + sin theta = cosec theta​

Answer 1

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Prove that

$\tt \frac{ {cos}^{2}\theta }{sin\theta} + sin \theta = cosec \theta$

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Taking LHS

$\tt \: LHS = \frac{ {cos}^{2} \theta }{sin \theta} + sin \theta \\ \\ \tt \: (taking \: LCM) \\ \\ \tt \: = \frac{ {cos}^{2} \theta + {sin}^{2} \theta }{sin \theta} \\ \\ \tt \: using \: identity \: \\ \tt {sin}^{2} \alpha + {cos}^{2} \alpha = 1 \\ \\ \tt \: = \frac{1}{sin \theta} \\ \\ \tt \: = cosec \theta \: = RHS$

Hence proved.