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Question

If x=a sec θ+b tan θ and y=a tan θ+b sec θ, then x2−y2a2−b2= ___

A

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B

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C

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D

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Solution

The correct option is B 1 x=a sec θ+b tan θ, y=a tan θ+b sec θ Squaring both sides we get, x2=(a sec θ+b tan θ)2, y2=(a tan θ+b sec θ)2 ∴x2=a2 sec2 θ+2ab sec θ tan θ+b2 tan2 θy2=a2 tan2 θ+2ab sec θ tan θ+b2 sec2 θ− − − –––––––––––––––––––––––––––––––––––––––––––––Subtracting, x2−y2=a2(sec2 θ−tan2 θ)+b2(tan2 θ−sec2 θ) x2−y2=a2(sec2 θ−tan2 θ)−b2(sec2 θ−tan2 θ) x2−y2=a2−b2……(sec2 θ−tan2 θ=1) ∴x2−y2a2−b2=1

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