`"Find "(dy)/(dx) if x =a(theta- sin theta) and y= a (1- cos theta).`

Explanation

`"We have "x=a(theta-sin theta)and y=a (1- cos theta).`
`therefore" "(dx)/("d"theta)=a(1-cos theta) and (dy)/("d"theta)=a sin theta`
`"or "(dy)/(dx)=(dy//"d" theta)/(dx//"d" theta)`
`=(a sin theta)/(a(1-cos theta))`
`=(2sin (theta//2)cos (theta//2))/(2 sin^(2) (theta//2))`
`=cot""(theta)/(2)`