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If x=-a(theta-sin theta),y=a(1-cos theta...

If `x=-a(theta-sin theta),y=a(1-cos theta),` then `(dy)/(dx)` is

A

`cot ""(theta)/(2)`

B

`tan ""(theta)/(2)`

C

`(1)/(2) "cosec"^(2) (theta)/(2) `

D

`- (1)/(2) "cosec "^(2) (theta)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given , ` x =a ( theta - sin theta)`
and ` y = a (1 - cos theta)`
`(d theta )/(d theta) = a (1 - cos theta)`
and ` (dy)/(d theta ) = a sin theta`
`therefore (dy)/(dx) = (a sin theta)/(a (1 - cos theta)) = (2 sin"" (theta)/(2)cos ""(theta)/(2))/( 2 sin^(2) ""(theta)/(2))= cot ""(theta)/(2)` .
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -EXERCISE 1 (DERIVATIVE OF IMPLICIT FUNCTION)
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