If $\alpha $ and $\beta $ are the roots of the quadratic equation, $x^2 + x\, sin\,\theta  -2sin\,\theta  = 0$, $\theta  \in \left( {0,\frac{\pi }{2}} \right)$ then $\frac{{{\alpha ^{12}} + {\beta ^{12}}}}{{\left( {{\alpha ^{ - 12}} + {\beta ^{ - 12}}} \right){{\left( {\alpha  - \beta } \right)}^{24}}}}$ is equal to

  • [JEE MAIN 2019]
  • A

    $\frac{{{2^{12}}}}{{{{\left( {\sin \,\theta  + 8} \right)}^{12}}}}$

  • B

    $\frac{{{2^{12}}}}{{{{\left( {\sin \,\theta  - 4} \right)}^{12}}}}$

  • C

    $\frac{{{2^{12}}}}{{{{\left( {\sin \,\theta  - 8} \right)}^{6}}}}$

  • D

    $\frac{{{2^{6}}}}{{{{\left( {\sin \,\theta  + 8} \right)}^{12}}}}$

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  • [KVPY 2017]

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  • [KVPY 2011]

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