Question

Let x₁, x₂, x₃, x₄ be four non zero numbers satisfying the equation

tan^-1(a/x) + (tan^-1(b/x) + tan^-1(c/x) tan^-1(d/x) = π then prove that

Answer 1

Given equation is

tan^-1(a/x) + (tan^-1(b/x) + tan^-1(c/x) tan^-1(d/x) = π

since x₁, x₂, x₃, x₄ are the values of the above equation,

we have