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Here x2 = a2 sec2 θ + 2ab sec θ tan θ + b2 tan2 θ
y2 = a2 tan2 θ + 2 ab sec θ tan θ + b2 sec2 θ
⇒ x2 – y2 = a2(sec2 θ – tan2 θ) – b2 (sec2 θ – tan2 θ)
= a2 – b2 (∵ sec2 θ – tan2 θ = 1)
Hence proved.
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