Q.

The slope of the normal to the curve x=a(cos θ+θsinθ) y=a(sinθ−θcosθ) at any pointθ is

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a

tanθ

b

cotθ

c

−tanθ

d

−cotθ

answer is A.

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Detailed Solution

dxdθ=a(−sinθ+θcosθ+sinθ) anddydθ=a(cosθ+θsinθ−cosθ) Hencedydx=(dydθ)/(dxdθ)=aθsinθaθcosθ=tanθ .
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The slope of the normal to the curve x=a(cos θ+θsinθ) y=a(sinθ−θcosθ) at any pointθ is