If \({\Delta _1} = \left| {\begin{array}{*{20}{c}}
  x&{\sin \,\theta }&{\cos \,\theta } \\ 
  {\sin \,\theta }&{ - x}&1 \\ 
  {\cos \,\theta }&1&x 
\end{array}} \right|\) and \({\Delta _1} = \left| {\begin{array}{*{20}{c}}
  x&{\sin \,2\theta }&{\cos \,\,2\theta } \\ 
  {\sin \,2\theta }&{ - x}&1 \\ 
  {\cos \,\,2\theta }&1&x 
\end{array}} \right|\), \(x \ne 0\) ; then for all \(\theta  \in \left( {0,\frac{\pi }{2}} \right)\)

1. A \({\Delta _1} - {\Delta _2} =  - 2{x^3}\)
2. B \({\Delta _1} + {\Delta _2} =  - 2({x^3} + x - 1)\)
3. C \({\Delta _1} - {\Delta _2} = x\left( {\cos \,2\theta  - \cos \,4\theta } \right)\)
4. D \({\Delta _1} + {\Delta _2} =  - 2{x^3}\)