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

Question

Find dy/dx, when x = cos^-1\(\cfrac{1}{1+t^2}\), y = sin^-1\(\cfrac{1}{1+t^2}\)

cos^-1 1/√(1 + t²), sin^-1 t/√(1 + t²)

Answer 1

Theorem: y and x are given in a different variable that is t. We can find dy/dx by finding dy/dt and dx/dt and then dividing them to get the required thing.