Prove that : \(\cot\theta + \tan\theta = \text{cosec}\,\theta \sec\theta\).

Q.2 (B)(5) Prove that : \(\cot\theta + \tan\theta = \text{cosec}\,\theta \sec\theta\).

Doubtly AI Asked 27 Oct 2026 AI-generated · not yet verified ssc 10th Save WhatsApp Report

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Answer: Proved below.

L.H.S. \(= \cot\theta + \tan\theta = \dfrac{\cos\theta}{\sin\theta} + \dfrac{\sin\theta}{\cos\theta}\)

\(= \dfrac{\cos^2\theta + \sin^2\theta}{\sin\theta\cos\theta} = \dfrac{1}{\sin\theta\cos\theta}\)

\(= \dfrac{1}{\sin\theta} \times \dfrac{1}{\cos\theta} = \text{cosec}\,\theta \sec\theta\) = R.H.S.

Doubtly AI · 27 Oct 2026 AI-generated · not yet verified Report

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