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# Solution for Find an Angle θ Whose Rate of Increase Twice is Twice the Rate of Decrease of Its Cosine ? - CBSE (Science) Class 12 - Mathematics

ConceptRate of Change of Bodies Or Quantities

#### Question

Find an angle θ whose rate of increase twice is twice the rate of decrease of its cosine ?

#### Solution

$\text { Let x } = \cos\theta$

$\text { Differentiating both sides with respect to t, we get }$

$\frac{d x}{d t} = \frac{d \left( \cos\theta \right)}{d t}$

$= - \sin\theta\frac{d \theta}{d t}$

$\text { But it is given that } \frac{d \theta}{d t} = - 2\frac{d x}{d t}$

$\Rightarrow \frac{d x}{d t} = - \sin\theta\left( - 2\frac{d x}{d t} \right)$

$\Rightarrow \sin\theta = \frac{1}{2}$

$\Rightarrow \theta = \frac{\pi}{6}$

$\text { Hence }, \theta = \frac{\pi}{6} .$

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Solution Find an Angle θ Whose Rate of Increase Twice is Twice the Rate of Decrease of Its Cosine ? Concept: Rate of Change of Bodies Or Quantities.
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