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If $x$ and $y$ are connected parametrically by the given equations, without eliminating the parameter. Find $\frac{d y}{d x}$
$x=a \sec \theta, y=b \tan \theta$
$x=a \sec \theta, y=b \tan \theta$
Solution:
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Verified Answer
$\frac{d x}{d \theta}=a \sec \theta \tan \theta$ and $\frac{d y}{d \theta}=b \sec ^2 \theta$
$\frac{d y}{d x}=\frac{b \sec ^2 \theta}{a \sec \theta \tan \theta}=\frac{b}{a} \operatorname{cosec} \theta$
$\frac{d y}{d x}=\frac{b \sec ^2 \theta}{a \sec \theta \tan \theta}=\frac{b}{a} \operatorname{cosec} \theta$
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