Chapter: Trigonometry· Mathematics Part 2 (Geometry)

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

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Answer: Proved.

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

\(= \dfrac{1}{\sin\theta} \times \dfrac{1}{\cos\theta} = \operatorname{cosec}\theta\,\sec\theta\) = RHS.

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report

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

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