Prove that: cot²θ – tan²θ = cosec²θ – sec²θ

Doubtly Asked 24 Oct 2026 Save WhatsApp Report

1 answer

Answer: LHS simplifies to RHS, as shown below.

Using \(\cot^2\theta=\csc^2\theta-1\) and \(\tan^2\theta=\sec^2\theta-1\):

\[\text{LHS}=(\csc^2\theta-1)-(\sec^2\theta-1)\]

\[=\csc^2\theta-\sec^2\theta=\text{RHS}\]

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

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