If `x=a(theta+sintheta)` and `y=a(1-costheta)`, find `dy//dx`.

Answer

`tan theta//2`

Explanation

`(dx)/(d theta) = a[1 - cos theta] , (dy)/(d theta) = a(0 +sin theta) = a sin theta.`
`:. (dy)/(dx) = (dy//d theta)/(dx // d theta) = (a sin theta)/(a (1 +cos theta))= (2sin theta// 2 cos tehta//2)/(2cos^2 theta//2) = tan theta//2`