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If cos ^(-1) x - cos ^(-1) ""( y )/(2) ...

If `cos ^(-1) x - cos ^(-1) ""( y )/(2) = alpha`, where ` -1 le x le 1, -2 le y le 2, x le (y)/(2)`, then for all `x and y`, `4x^(2) - 4xy cos alpha + y^(2)` is equal to

A

`2"sin"^(2)alpha`

B

`4"sin"^(2)alpha-2x^(2)y^(2)`

C

`4cos^(2)alpha+2x^(2)y^(2)`

D

`4"sin"^(2)alpha`

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The correct Answer is:
D
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