1.

If `x=cost, y=sint,` then what is `(d^(2)y)/(dx^(2))` equal to?A. `y^(-3)`B. `y^(3)`C. `-y^(-3)`D. `-y^(3)`

Answer» Correct Answer - C
Given that `x=cost, y=sint`
`rArr" "(dx)/(dt)-sint and (dy)/(dt)=cot`
`rArr" "(dy)/(dx)=((dy)/(dt))/((dx)/(dt))=-(cost)/(sint)rArr (dy)/(dx)=-cot t`
`rArr" "(d^(2)y)/(dx^(2))="cosec"^(2)t.(dt)/(dx)="cosec"^(2)t.(1)/(-sint)=(1)/(sin^(3)t)`
`rArr" "(d^(2)y)/(dx^(2))=-y^(-3)`


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