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If $x$ and $y$ are connected parametrically by the given equations, without eliminating the parameter. Find $\frac{d y}{d x}$
$x=\sin \mathrm{t}, \mathrm{y}=\cos 2 \mathrm{t}$
$x=\sin \mathrm{t}, \mathrm{y}=\cos 2 \mathrm{t}$
Solution:
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Verified Answer
$\therefore \frac{d x}{d t}=\cos t$ and $\frac{d y}{d t}=-\sin 2 t \cdot 2=-2 \sin 2 t$
$\frac{d y}{d x}=\frac{-2 \sin 2 t}{\cos t}=\frac{-2 \cdot 2 \sin t \cos t}{\cos t}=-4 \sin t$
$\frac{d y}{d x}=\frac{-2 \sin 2 t}{\cos t}=\frac{-2 \cdot 2 \sin t \cos t}{\cos t}=-4 \sin t$
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