JEE Math Practice Question

If $${\Delta _1} = \left| {\begin{matrix} x & {\sin \theta } & {\cos \theta } \\ { - \sin \theta } & { - x} & 1 \\ {\cos \theta } & 1 & x \\ \end{matrix} } \right|$$ and $${\Delta _2} = \left| {\begin{matrix} x & {\sin 2\theta } & {\cos 2\theta } \\ { - \sin 2\theta } & { - x} & 1 \\ {\cos 2\theta } & 1 & x \\ \end{matrix} } \right|$$, $$x \ne 0$$ ; then for all $$\theta \in \left( {0,{\pi \over 2}} \right)$$ :

1. A.$${\Delta _1} - {\Delta _2}$$ = x (cos 2$$\theta $$ – cos 4$$\theta $$)
2. B.$${\Delta _1} + {\Delta _2}$$ = - 2x3
3. C.$${\Delta _1} + {\Delta _2}$$ = – 2(x3 + x –1)
4. D.$${\Delta _1} - {\Delta _2}$$ = - 2x3