Question

Find the value of the following: tan1/2[sin^-1(2x/(1 + x²)) + cos^-1((1 - y²)/(1 + y²)], |x| < 1, y > 0 and xy < 1

Answer 1

Let x = tanα and y = tanβ ⇒ α = tan^-1x, β = tan^-1y