Question

If x=a(Theta+sin theta) & y=a(1+cos theta) , find dy/dx​

Answer 1

x=a(θ+sinθ)

$\bf \frac{dx}{dθ} = a(1 + cosθ) \: \: \: \: \: \: (1)$

y=a(1−cosθ)

$\bf \: \frac{dy}{dθ} = a(0 - ( - sinθ)) = a \: sinθ \: \: \: \: (2)$

$\bf \: Dividing (2) and (1)  \frac{dy/dθ}{dx/dθ} = \frac{dy}{dx} = \frac{sinθ}{1 + cosθ}tan(θ/2)$