Find dy/dx, when If x = 2cos θ - cos 2θ and y = 2sin θ - sin 2θ, prove that dy/dx = tan(3θ/2).

Question

Find \(\cfrac{dy}{d\mathrm x} \), when

If x = 2cos θ - cos 2θ and y = 2sin θ - sin 2θ, prove that \(\cfrac{dy}{d\mathrm x} \) = tan\(\Big(\cfrac{3\,\theta}{2}\Big).\).

Answer 1

as x = 2cos θ – cos 2θ

Differentiating it with respect to θ using chain rule,

And, y = 2sin θ – sin 2θ

Differentiating it with respect to using chain rule,

dividing equation (2) by equation (1),