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

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

Answer»

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

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

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