If x = cos θ (1 + cos θ) and y = sinθ(1 + cosθ) then (\dy/\dx)_{\theta=\\pi/2} =

TS ICET 24 May 2018 Shift 1 Paper

Question : 135 of 200

Marks: +1, -0

If x = cos θ (1 + cos θ) and y = sinθ(1 + cosθ) then

(\dy/\dx)_{θ=\π/2}

Solution:

x=\cos θ(1+\cos θ)

\;{d x}/{d θ}=\cos θ(-\sin θ)+(1+\cos θ)(-\sin θ)

y=\sin θ(1+\cos θ)

\;{d y}/{d θ}=\sin θ(-\sin θ)+(1+\cos θ) \cos θ

{d y}/{d x}={{d y}/{d x}}/{{d x}/{d f}}={-\sin ^{2} θ+(1+\cos θ) \cos θ}/{-\cos θ \sin θ-(1+\cos θ) \sin θ}

(\;{d y}/{d x})_{θ=\;{π}/{2}}=\;{-1+0}/{0-(1+0) 1}

=\;{-1}/{-1}=1

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