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Prove that: sin^(-1){(sqrt(1+x)+sqrt(1-x...

Prove that: `sin^(-1){(sqrt(1+x)+sqrt(1-x))/2}=pi/2-(sin^(-1)x)/2,""0 < x < 1`

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To prove the equation \[ \sin^{-1}\left(\frac{\sqrt{1+x} + \sqrt{1-x}}{2}\right) = \frac{\pi}{2} - \frac{\sin^{-1}x}{2}, \quad 0 < x < 1, \] we will start with the left-hand side (LHS) and manipulate it to show that it equals the right-hand side (RHS). ...
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