Prove That !! cos^-1x = 2sin^-1 root of(1-x/2)

Please help me with this problem.. i couldnt even get anything nearer to it.

To Prove : cosֿ¹ x = 2 · sinֿ¹ √[ ( 1 - x ) / 2 ].
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On the RHS,

let : x = cos 2Φ.

∴ 2Φ = cosֿ¹ x ........................................… (1)

∴√[ (1-x) / 2] = √[ ( 1 - cos 2Φ ) / 2 ]

. . . . . . . . . . . = √[ ( 2 sin² Φ ) / 2 ]

. . . . . . . . . . . = sin Φ.
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∴ RHS

= 2 · sinֿ¹ √[ (1-x) / 2 ]

= 2 · sinֿ¹ ( sin Φ )

= 2 · Φ

= ( 2Φ )

= cosֿ¹ x ............... from (1)

= LHS ........................................… Q.E.D.
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Happy To Help !
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