Write the given expression in terms of x and y only. tan(sin^−1(x) + cos^−1(y))

Answer 1

Let θ = sin^-1x and φ = cos^-1y Note that tanθ = x/sqrt(1-x²) and tanφ = sqrt(1-y²)/y by making the theta triangle have height x and hypotenuse 1 and the phi triangle have base y and hypotenuse 1.

tan(θ+φ) = (tanθ + tanφ)/(1-tanθtanφ)

Now sub in and simplify the mess.