If x=a(1-cos theta) and y=a(theta+sin theta), | vedclass

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(C) Given $x = a(1 - \cos 	heta)$ and $y = a(	heta + \sin 	heta)$.First,differentiate $x$ with respect to $	heta$:$\frac{dx}{d	heta} = a(0 - (-\s

Vedclass · Accepted Answer

$\cot \frac{	heta}{2}$

Vedclass · Answer

(C) Given $x = a(1 - \cos 	heta)$ and $y = a(	heta + \sin 	heta)$.First,differentiate $x$ with respect to $	heta$:$\frac{dx}{d	heta} = a(0 - (-\sin 	heta)) = a \sin 	heta$.Next,differentiate $y$ with respect to $	heta$:$\frac{dy}{d	heta} = a(1 + \cos 	heta)$.Now,find $\frac{dy}{dx}$ using the chain rule:$\frac{dy}{dx} = \frac{dy/d	heta}{dx/d	heta} = \frac{a(1 + \cos 	heta)}{a \sin 	heta} = \frac{1 + \cos 	heta}{\sin 	heta}$.Using trigonometric identities $1 + \cos 	heta = 2 \cos^2 \frac{	heta}{2}$ and $\sin 	heta = 2 \sin \frac{	heta}{2} \cos \frac{	heta}{2}$:$\frac{dy}{dx} = \frac{2 \cos^2 \frac{	heta}{2}}{2 \sin \frac{	heta}{2} \cos \frac{	heta}{2}} = \frac{\cos \frac{	heta}{2}}{\sin \frac{	heta}{2}} = \cot \frac{	heta}{2}$.Thus,the correct option is $C$.

If $x=a(1-\cos \theta)$ and $y=a(\theta+\sin \theta)$,then $\frac{dy}{dx} =$ . . . . . .

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