If x = a(cos θ + θ sin θ ) and y = a(sin θ - θ cos θ), show that d^2y/dx^2 = 1/a(sec^3 θ)/θ

Question

If x = a(cos θ + θ sin θ ) and y = a(sin θ - θ cos θ), show that \(\cfrac{d^2y}{d\text x^2}=\cfrac1a\left(\cfrac{sec^3\theta}{\theta}\right)\)

d²y/dx² = 1/a(sec³ θ)/θ

Answer 1

Differentiating with respect to θ

Differentiating with respect to x

Hence Proved