Find frac{dy}{dx} for the equation sin^{2} x | vedclass

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Question

(A) Given the equation: $\sin^{2} x + \cos^{2} y = 1$. Differentiating both sides with respect to $x$: $\frac{d}{dx}(\sin^{2} x) + \frac{d}{dx}(\cos^{

Vedclass · Accepted Answer

$\frac{\sin 2x}{\sin 2y}$

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(A) Given the equation: $\sin^{2} x + \cos^{2} y = 1$. Differentiating both sides with respect to $x$: $\frac{d}{dx}(\sin^{2} x) + \frac{d}{dx}(\cos^{2} y) = \frac{d}{dx}(1)$ Using the chain rule: $2 \sin x \cos x + 2 \cos y (-\sin y) \frac{dy}{dx} = 0$ Using the identity $\sin 2	heta = 2 \sin 	heta \cos 	heta$: $\sin 2x - \sin 2y \frac{dy}{dx} = 0$ Rearranging to solve for $\frac{dy}{dx}$: $\sin 2y \frac{dy}{dx} = \sin 2x$ $\frac{dy}{dx} = \frac{\sin 2x}{\sin 2y}$

Find $\frac{dy}{dx}$ for the equation $\sin^{2} x + \cos^{2} y = 1$.

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