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Question

If x = a cos θ,y=b sin θ,then d3ydx3 is equal to

A
(3ba3)cosec4θ cot4θ
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B
(3ba3)cosec4θ cotθ
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C
(3ba3)cosec4θ cotθ
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D
None of the above
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Solution

The correct option is C (3ba3)cosec4θ cotθ
x=acosθdxdθ=a sin θ and y=b sin θ dydθ=b cos θdydx=ba cot θd2ydx2=ba cosec2θ dθdx=ba2cosec3θd3ydx3=3ba2 cosec2θ(cosec θ cot θ)dθdx=3ba2 cosec3θ cot θ (1a sin θ)=3ba3 cosec4θ cot θ

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