AP ICET 2016 Paper

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Question : 113 of 200

Marks: +1, -0

If

x=\sinθ+θ\cosθ

and

y=\cosθ-θ\sinθ,

then

{dy}/{dx}

at

θ=π/2

is

$4/π$
$π/4$
$2/π$
${-π}/2$

Solution:

Given :

x=\sinθ+θ\cosθ,y=\cosθ–θ\sinθ

{dx}/{dθ}=\cosθ+\cosθ+θ(-\sinθ)

,and

{dy}/{dθ}=-\sinθ-(\sinθ+θ\cosθ)

{dy}/{dx}={dy{/}dθ}/{dx{/}dθ}={2\sinθ-θ\cosθ}/{2\cosθ-θ\sinθ}

({dy}/{dx})_{θ={π}/{2}}=({-2-0}/{0-\;\;{π}/{2}})={4}/{π}

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