Question

x= 2 (theta+sin theta) and y=2 (1-cos theta) then, dy/dx

Answer 1

Answer:dy/dx= tan (theta/2).

Explanation:

Answer 2

$\dfrac{dy}{dx}=\dfrac{\sin\theta}{1+\cos\theta}$

Explanation:

Given that,

$x=2(\theta+\sin\theta)$.........(1)

$y=2(1-\cos\theta)$.........(2)

It is required to find $\dfrac{dy}{dx}$

Differentiating equation (1) wrt $\theta$.

$\dfrac{dx}{d\theta}=2\dfrac{d(\theta+\sin\theta)}{d\theta}\\\dfrac{dx}{d\theta}=2(1+\cos\theta)..........(3)$

Differentiating equation (2) wrt $\theta$.

$\dfrac{dy}{d\theta}=2\dfrac{d(1-\cos\theta)}{d\theta}\\\dfrac{dy}{d\theta}=2\sin\theta..........(4)$

Now,

$\dfrac{dy}{dx}=\dfrac{dy}{d\theta}\times \dfrac{d\theta}{dx}\\\\\dfrac{dy}{dx}=2\sin\theta \times \dfrac{1}{2(1+\cos\theta)}\\\\\dfrac{dy}{dx}=\dfrac{\sin\theta}{1+\cos\theta}$

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Differentiation

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