Question
If x=a sec θ+b tan θ and y=a tan θ+b sec θ, then x2−y2a2−b2= ___
Answer: Option B
:
B
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B
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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