If x and y are connected parametrically by th | vedclass

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(A) Given equations are $x = a(\cos 	heta + 	heta \sin 	heta)$ and $y = a(\sin 	heta - 	heta \cos 	heta)$.First,differentiate $x$ with respect t

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$	an 	heta$

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(A) Given equations are $x = a(\cos 	heta + 	heta \sin 	heta)$ and $y = a(\sin 	heta - 	heta \cos 	heta)$.First,differentiate $x$ with respect to $	heta$:$\frac{dx}{d	heta} = a \left[ \frac{d}{d	heta}(\cos 	heta) + \frac{d}{d	heta}(	heta \sin 	heta) ight]$$= a [-\sin 	heta + (	heta \cos 	heta + \sin 	heta \cdot 1)]$$= a [-\sin 	heta + 	heta \cos 	heta + \sin 	heta] = a 	heta \cos 	heta$.Next,differentiate $y$ with respect to $	heta$:$\frac{dy}{d	heta} = a \left[ \frac{d}{d	heta}(\sin 	heta) - \frac{d}{d	heta}(	heta \cos 	heta) ight]$$= a [\cos 	heta - (	heta(-\sin 	heta) + \cos 	heta \cdot 1)]$$= a [\cos 	heta + 	heta \sin 	heta - \cos 	heta] = a 	heta \sin 	heta$.Now,find $\frac{dy}{dx}$ using the chain rule:$\frac{dy}{dx} = \frac{dy/d	heta}{dx/d	heta} = \frac{a 	heta \sin 	heta}{a 	heta \cos 	heta} = 	an 	heta$.

If $x$ and $y$ are connected parametrically by the equations,without eliminating the parameter,find $\frac{dy}{dx}$ for $x = a(\cos \theta + \theta \sin \theta)$ and $y = a(\sin \theta - \theta \cos \theta)$.

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