${(\cos \alpha + \cos \beta )^2} + {(\sin \alpha + \sin \beta )^2} = $

  • A

    $4{\cos ^2}\frac{{\alpha - \beta }}{2}$

  • B

    $4{\sin ^2}\frac{{\alpha - \beta }}{2}$

  • C

    $4{\cos ^2}\frac{{\alpha + \beta }}{2}$

  • D

    $4{\sin ^2}\frac{{\alpha + \beta }}{2}$

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  • [IIT 2001]

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