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Question
Prove that cot2θ – tan2θ = cosec2θ – sec2θ.
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Solution
L.H.S. = cot2θ – tan2θ
= (cosec2θ – 1) – (sec2θ – 1) ...`[(∵ tan^2θ = sec^2θ - 1),(cot^2θ = "cosec"^2θ - 1)]`
= cosec2θ – 1 – sec2θ + 1
= cosec2θ – sec2θ
= R.H.S.
∴ cot2θ – tan2θ = cosec2θ – sec2θ
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