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# Find D Y D X , When X = B Sin 2 θ and Y = a Cos 2 θ ? - CBSE (Arts) Class 12 - Mathematics

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ConceptSimple Problems on Applications of Derivatives

#### Question

Find $\frac{dy}{dx}$ , when $x = b \sin^2 \theta \text{ and } y = a \cos^2 \theta$ ?

#### Solution

$\text{ We have, x } = b \sin^2 \theta \text{ and } y = a \cos^2 \theta$

$\therefore \frac{dx}{d\theta} = \frac{d}{d\theta}\left( b \sin^2 \theta \right) = 2b \sin\theta\cos\theta$

$\text{ and },$

$\frac{dy}{d\theta} = \frac{d}{d\theta}\left( a \cos^2 \theta \right) = - 2a \cos\theta\sin\theta$

$\therefore \frac{dy}{dx} = \frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}} = \frac{- 2a \cos\theta\sin\theta}{2b \sin\theta\cos\theta} = - \frac{a}{b}$

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Solution Find D Y D X , When X = B Sin 2 θ and Y = a Cos 2 θ ? Concept: Simple Problems on Applications of Derivatives.
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