`x=a(costheta+ theta sintheta), y=a(sin theta- theta cos theta)`

Explanation

`x = a (costheta+thetasintheta) ,y=a(sintheta-thetacostheta)`
Differentiating x and y w.r.t. `theta`, we get,
`(dx)/(d theta)=a(d)/(d theta)(costheta+thetasintheta)`
`=a[(d)/(d theta)(costheta)+(d)/(d theta)(thetasintheta)]`
`=a[-sin theta+thetacostheta+sinthetaxx1]=athetacostheta`
`and(dy)/(d theta)=a(d)/(d theta)(sintheta-thetacostheta)`
`=a[(d)/(d theta)(sintheta)-(d)/(d theta)(thetacostheta)]`
`=a[costheta-{theta(d)/(d theta)(costheta)+costheta(d)/(d theta)(theta)}]`
`=a[costheta-{theta(-sintheta)+costhetaxx1}]`
`=a[costheta+thetasintheta-costheta]=athetasintheta`