If $\alpha ,$ $\beta$ are different values of $x$ satisfying $a\cos x + b\sin x = c,$ then $\tan {\rm{ }}\left( {\frac{{\alpha + \beta }}{2}} \right) = $

  • A

    $a + b$

  • B

    $a - b$

  • C

    $\frac{b}{a}$

  • D

    $\frac{a}{b}$

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