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  • <img alt="\text { If } x=\cos \theta \text { and } y=\sin ^3 \theta \text {, then }\left|\frac{y d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^2\right| \text { at } \theta=\frac{\pi}{2} \text { is }"

\text { If } x=\cos \theta \text { and } y=\sin ^3 \theta \text {, then }\left|\frac{y d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^2\right| \text { at } \theta=\frac{\pi}{2} \text { is }

Option: 1

2.5


Option: 2

4


Option: 3

3


Option: 4

4.5


Answers (1)

best_answer

\mathrm{\begin{aligned} & \text { } \frac{d y}{d x}=\frac{d y}{d \theta} \div \frac{d x}{d \theta}=-3 \sin \theta \cos \theta \\ & \frac{d^2 y}{d x^2}=\frac{-3 \cos ^2 \theta+3 \sin ^2 \theta}{-\sin \theta} \end{aligned} }
\mathrm{\begin{aligned} \therefore\left|y y_2+y_1^2\right| & =3 \sin ^2 \theta\left(\cos ^2 \theta-\sin ^2 \theta\right)+9 \sin ^2 \theta \cos ^2 \theta \\ & =3 \text { at } \theta=\frac{\pi}{2} . \end{aligned} }

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Pankaj Sanodiya

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