Question

if x=2(θ+sinθ) and y=2(1-cosθ),then value of dy/dx is

Answer 1

${\mathcal{\red{ANSWER}}}$

Correction:

x = 2(1 + sinФ) will be there in place of x = 2(Ф + sinФ).

Given:

$\tt{x = 2(1+\sin\theta)}$

$\tt{y=2(1-\cos\theta)}$

To find:  $\tt{\dfrac{dy}{dx}}$

So,

$\tt{\implies \dfrac{dy}{do} =2(0+\sin\theta)}$

$\tt{\implies \dfrac{dx}{do} = 2(\cos\theta)}$

$\tt{\implies \dfrac{\dfrac{dy}{do}}{\dfrac{dx}{do}} = \dfrac{2\sin\theta}{2\cos\theta} = \tan\theta}$

$\tt{So,\;\dfrac{dy}{dx} = \tan\theta}$

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