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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

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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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