If `x=a\ (theta-sintheta),\ y=a\ (1+costheta),\ \ \ ` find `(d^2\ y)/(dx^2)`

Explanation

`y = a+acostheta`

`=>dy/(d theta) = - asin theta`

`x = atheta - asintheta`

`=>dy/(d theta) = a - acostheta = a( 1- costheta)`

`:. dy/dx = (dy/(d theta))/(dx/(d theta)) = (-asin theta)/(a(1-costheta))`

`=>dy/dx = -sintheta/(1-costheta)**(1+costheta)/(1+costheta)`

`=>dy/dx = -(sintheta (1+costheta))/(1-cos^2theta)`

`=>dy/dx = -(sintheta (1+costheta))/(sin^2theta)`

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