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Question

If x=a sec θ+b tan θ and y=a tan θ+b sec θ, then x2y2a2b2= ___


A

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B

1

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C

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D

- 1

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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, x2y2=a2(sec2 θtan2 θ)+b2(tan2 θsec2 θ)

x2y2=a2(sec2 θtan2 θ)b2(sec2 θtan2 θ)

x2y2=a2b2(sec2 θtan2 θ=1)

x2y2a2b2=1


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