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Question

If x=secθcosθ and y=secnθcosnθ, then (dydx)2 is equal to

A
n2(y2+4)x2+4
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B
n2(y24)x2
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C
n(y24x2+4)
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D
(nyx)24
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Solution

The correct option is A n2(y2+4)x2+4
x=secθcosθ
dxdθ=secθtanθ+sinθ
=tanθ(secθ+cosθ)
y=secnθcosnθ
dydθ=nsecn1θsecθtanθ+ncosn1θsinθ
=ntanθ(secnθ+cosnθ)
dydx=ntanθ(secnθ+cosnθ)tanθ(secθ+cosθ)
=n(secnθcosnθ)2+4(secθcosθ)2+4
=ny2+4x2+4
(dydx)2=n2(y2+4)x2+4

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