Find dy/dx if x = cos^-1(2t/(1 + t^2)), y = sec^-1(√(1 + t^2))

Question

Find dy/dx if

x = \(cos^{-1}\left(\frac{2t}{1 + t^2}\right), y = sec^{-1}(\sqrt{1 + t^2})\)

x = cos^-1(2t/(1 + t²)), y = sec^-1(√(1 + t²))

Answer 1

x = cos^-1(2t/(1 + t²)), y = sec^-1(√(1 + t²))

Put t = tan θ Then θ = tan^-1t

Differentiating x and y w.r.t. t, we get