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Question

If x=secθcosθ,y=sec10θcos10θ and (x2+4)(dydx)2=k(y2+4), then k is equal to

A
1100
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B
1
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C
10
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D
100
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Solution

The correct option is D 100
x2+4=(secθcosθ)2+4=(secθ+cosθ)2 (i)Similarly,y2+4=(sec10θ+cos10θ)2 (ii)Now,dxdθ=secθtanθ+sinθ=tanθ(secθ+cosθ)and dydθ=10sec9θsecθtanθ10cos9θ(sinθ)=10tanθ(sec10θcos10θ)dydx=(dydθ)(dxdθ)=10tanθ(sec10θ+cos10θ)tanθ(secθ+cosθ)(dydx)2=100(sec10θ+cos10θ)(secθ+cosθ)2=100(y2+4)(x2+4)or (x2+4)(dydx)2=100(y2+4)
On comparing with the expression given we get k = 100

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