Question

If x = 2 cos θ – cos 2θ and y = 2 sin θ – sin 2θ, then `dy/dx` is ______.

Options

• `(cosθ + cos2θ)/(sinθ - sin2θ_`

• `(cosθ - cos2θ)/(sin2θ - sinθ)`

• `(cosθ - cos2θ)/(sinθ - sin2θ)`

• `(cos2θ - cosθ)/(sin2θ + sinθ)`

Answer 1

If x = 2 cos θ – cos 2θ and y = 2 sin θ – sin 2θ, then `dy/dx` is `underlinebb((cosθ - cos2θ)/(sin2θ - sinθ))`.

Explanation:

Given, x = 2 cos θ – cos 2θ

And y = 2 sin θ – sin 2θ

Therefore, `dx/(dθ) = -2 sin θ + 2 sin 2θ`

And `dy/(dθ) = 2 cos θ - 2 cos 2θ`

∴ `dy/dx = (2 cos θ - 2 cos 2θ)/(-2 sin θ + 2 sin 2θ)`

or `dy/dx = (cos θ - cos 2θ)/(sin 2θ - sin θ)`