If x = a√(sec θ - tan θ), x = a√(sec θ + tan θ), then show that dy/dx = - y/x

Question

If x = \(a\sqrt{sec\,\theta - tan\,\theta},\, y = a\sqrt{sec\,\theta + tan\,\theta},\) then show that dy/dx = - y/x

If x = a√(sec θ - tan θ), x = a√(sec θ + tan θ),

Answer 1

x = a√(sec θ - tan θ), x = a√(sec θ + tan θ)

Adding (1) and (2), we get

Subtracting (1) from (2), we get

differentiating both sides w.r.t. x, we get