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LHS \(= \sec^2\theta + \text{cosec}^2\theta\)

\[= \frac{1}{\cos^2\theta} + \frac{1}{\sin^2\theta}\]\[= \frac{\sin^2\theta + \cos^2\theta}{\cos^2\theta \, \sin^2\theta}\]\[= \frac{1}{\cos^2\theta \, \sin^2\theta} \quad (\because \sin^2\theta + \cos^2\theta = 1)\]\[= \frac{1}{\cos^2\theta} \times \frac{1}{\sin^2\theta} = \sec^2\theta \times \text{cosec}^2\theta\]

= RHS

\(\therefore \sec^2\theta + \text{cosec}^2\theta = \sec^2\theta \times \text{cosec}^2\theta\)

Doubtly AI · 4 Nov 2026 AI-verified · Nov 2026 Report
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