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If x=(1+logt)/(t^2),\ \ y=(3+2logt)/t ,\...

If `x=(1+logt)/(t^2),\ \ y=(3+2logt)/t ,\ \ ` find `(dy)/(dx)` .

A

`tan theta `

B

`cot theta `

C

`sin theta `

D

`cos theta `

Text Solution

Verified by Experts

The correct Answer is:
A
Given , ` x = a (cos theta + theta sin theta ), y = a (sin theta - theta cos theta)`
On differentiating both sides w.r.t.` theta ` , we get
`(dx)/(d theta ) = a { - sin theta + ( theta cos theta + sin theta . 1)} = a theta cos theta `
` and (dy)/(d theta ) = a [cos theta - {theta ( - sin theta ) + cos theta .1)} = atheta sin theta `
` therefore (dy)/(dx) = ((dy)/(d theta))/((d x)/(d theta))= (a theta sin theta )/(a theta cos theta)= tan theta ` .
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