If $A + B + C = {180^o},$ then $\frac{{\sin 2A + \sin 2B + \sin 2C}}{{\cos A + \cos B + \cos C - 1}} = $

  • A

    $8\,\sin \frac{A}{2}\sin \frac{B}{2}\sin \frac{C}{2}$

  • B

    $8\cos \frac{A}{2}\cos \frac{B}{2}\cos \frac{C}{2}$

  • C

    $8\,\sin \frac{A}{2}\cos \frac{B}{2}\cos \frac{C}{2}$

  • D

    $8\,\cos \frac{A}{2}\sin \frac{B}{2}\sin \frac{C}{2}$

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  • [JEE MAIN 2019]