If $x{\sin ^3}\alpha + y{\cos ^3}\alpha = \sin \alpha \cos \alpha $ and $x\sin \alpha - y\cos \alpha = 0,$ then ${x^2} + {y^2} = $

  • A

    $-1$

  • B

    $±1$

  • C

    $1$

  • D

    None of these

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