Find the value of dy/dx at θ =π /4 , if x = ae^θ(sin θ - cos θ) and y = ae^θ (sin θ + cos θ).

Question

Find the value of \(\frac{dy}{dx}\) at θ = \(\frac{\pi}{4}\), if x = ae^θ(sin θ - cos θ) and y = ae^θ (sin θ + cos θ).

Answer 1

Given,

x = ae^θ(sin θ - cos θ) and y = ae^θ (sin θ + cos θ)

x = ae^θ(sin θ - cos θ)

Differentiating with respect to q, we get

Again,

∵ y = ae^θ (sin θ + cos θ)

Differentiating with respect to θ, we get