Question

If sin^-1x + sin^-1y + sin^-1z = π, then prove that,

x(1 - x²) + y(1 - y²) + z(1 - z²) = 2xyz

Answer 1

Put A = sin^-1x, B = sin^-1y, C = sin^-1Z

x = sinA, y = sinB z = sinC

cosA = √(1 - x²), cosB = √(1 - y²), cosC = √(1 - z²)

Thus, A + B + C = π