Question
If x = a cos θ,y=b sin θ,then d3ydx3 is equal to
Answer: Option C
:
C
∵x=acosθ⇒dxdθ=−a sin θ and y=b sin θ ⇒dydθ=b cos θ∴dydx=−ba cot θ⇒d2ydx2=ba cosec2θ dθdx=−ba2cosec3θ∴d3ydx3=3ba2 cosec2θ(−cosec θ cot θ)dθdx=3ba2 cosec3θ cot θ (−1a sin θ)=−3ba3 cosec4θ cot θ
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:
C
∵x=acosθ⇒dxdθ=−a sin θ and y=b sin θ ⇒dydθ=b cos θ∴dydx=−ba cot θ⇒d2ydx2=ba cosec2θ dθdx=−ba2cosec3θ∴d3ydx3=3ba2 cosec2θ(−cosec θ cot θ)dθdx=3ba2 cosec3θ cot θ (−1a sin θ)=−3ba3 cosec4θ cot θ
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