Question

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

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

Answer 1

Let sin^-1 x = A ⇒ x = sin A

sin^-1 y = B ⇒ y = sin B

sin^-1 z = C ⇒ z = sin C

∵ sin^-1 x + sin^-1 y + sin^-1 z = π

∴ A + B + C = π

∴ To prove