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

• 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

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