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B
(3ba3)cosec4θcotθ
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C
(−3ba3)cosec4θcotθ
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D
None of the above
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Solution
The correct option is C(−3ba3)cosec4θcotθ ∵x=acosθ⇒dxdθ=−asinθandy=bsinθ⇒dydθ=bcosθ∴dydx=−bacotθ⇒d2ydx2=bacosec2θdθdx=−ba2cosec3θ∴d3ydx3=3ba2cosec2θ(−cosecθcotθ)dθdx=3ba2cosec3θcotθ(−1asinθ)=−3ba3cosec4θcotθ