Find `(dy)/(dx)` if `x=cos theta - cos 2 theta`
`and" "y = sin theta - sin 2theta`

Answer

`(cos theta -2 cos 2 theta)/(2 sin 2 theta - sin theta)`

Explanation

The given equations are `x=cos theta - cos 2 theta`
`and" "y = sin theta - sin 2theta`
`"Then, "(dx)/(d""theta)=-sin theta - (-2 sin 2theta)=2 sin 2 theta- sin theta`
`"And "(dy)/(d""theta)=cos theta -2 cos 2theta`
`therefore" "(dy)/(dx)=(dy//d""theta)/(dx//d""theta)=(cos theta-2 cos 2theta)/(2 sin 2theta- sin theta)`