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# Solution for If X = Cos T and Y = Sin T , Prove that D Y D X = 1 √ 3 at T = 2 π 3 ? - CBSE (Science) Class 12 - Mathematics

ConceptSimple Problems on Applications of Derivatives

#### Question

If $x = \cos t \text{ and y } = \sin t,$ prove that  $\frac{dy}{dx} = \frac{1}{\sqrt{3}} \text { at } t = \frac{2 \pi}{3}$ ?

#### Solution

$\text{ We have, x } = \cos t \text{ and y } = \sin t$
$\Rightarrow \frac{dx}{dt} = \frac{d}{dt}\left( \cos t \right) \text { and } \frac{dy}{dt} = \frac{d}{dt}\left( \sin t \right)$
$\Rightarrow \frac{dx}{dt} = - \sin t \text{ and } \frac{dy}{dt} = \cos t$
$\therefore \frac{\frac{dy}{dt}}{\frac{dx}{dt}} = \frac{\cos t}{- \sin t} = - \cot t$
$\text{ Now,} \left( \frac{dy}{dx} \right)_{t = \frac{2\pi}{3}} = - \cot \left( \frac{2\pi}{3} \right) = \frac{1}{\sqrt{3}}$
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Solution for question: If X = Cos T and Y = Sin T , Prove that D Y D X = 1 √ 3 at T = 2 π 3 ? concept: Simple Problems on Applications of Derivatives. For the courses CBSE (Science), CBSE (Commerce), CBSE (Arts), PUC Karnataka Science
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