Answer :

To solve for x: sin^{-1} x + sin^{-1} (1 – x) = cos^{-1} x

Let cos^{-1} x = θ

⇒ x = cos θ

We know,

We have,

sin^{-1} x + sin^{-1} (1 – x) = cos^{-1} x

Put cos^{-1} x = θ:

⇒ sin^{-1} x + sin^{-1} (1 – x) = θ

**OR**

Squaring both sides:

**Hence Proved**

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