" 9.(i) "" Umi "x=a(theta+sin theta),y=a(1+cos theta)

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

(sin theta+i cos theta)^(9) =

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

" (i) "(cos theta+sin theta)/(cos theta-sin theta)

(i) |(cos theta,-sin theta),(sin theta,cos theta)|

Prove each of the following identities : (i) (1+ cos theta + sin theta)/(1+ cos theta - sin theta) =(1+ sin theta)/(cos theta) (ii) (sin theta + 1- cos theta)/(cos theta - 1 + sin theta) = (1+ sin theta)/(cos theta)

The normal to the curve x=a(cos theta + theta sin theta), y=a(sin theta - theta cos theta) at any theta is such that

The normal to the curve x=a(cos theta + theta sin theta), y=a(sin theta - theta cos theta) at any theta is such that

The normal to the curve x=a(cos theta + theta sin theta), y=a(sin theta - theta cos theta) at any theta is such that