Question

Prove that sin^-1 x + cos^-1 x = π/2, x ∈ [-1, 1].

Answer 1

Let sin^-1 x = θ then. 

x = sin θ ⇒ x = cos(π/2 - θ) 

⇒ cos^-1x = π/2 - θ ⇒ θ + cos^-1 x = π/2

∴ sin^-1 x + cos^-1 x = π/2