If \({{\rm{\Delta }}_1} = \left| {\begin{array}{*{20}{c}}{\rm{x}}&{{\rm{sin\theta }}}&{{\rm{cos\theta }}}\\{ - {\rm{sin\theta }}}&{ - {\rm{x}}}&1\\{{\rm{cos\theta }}}&1&{\rm{x}}\end{array}} \right|\) and \({{\rm{\Delta }}_2} = \left| {\begin{array}{*{20}{c}}{\rm{x}}&{{\rm{sin}}2{\rm{\theta }}}&{{\rm{cos}}2{\rm{\theta }}}\\{ - {\rm{sin}}2{\rm{\theta }}}&{ - {\rm{x}}}&1\\{{\rm{cos}}2{\rm{\theta }}}&1&{\rm{x}}\end{array}} \right|,{\rm{x}} \ne 0;\) then for all \({\rm{\theta }} \in \left( {0,\frac{{\rm{\pi }}}{2}} \right):\)

• A. Δ1 – Δ2 = -2x3
• B. Δ1 – Δ2 = x(cos 2θ – cos 4θ)
• C. Δ1 + Δ2 = -2(x3 + x – 1)
• D. Δ1 + Δ2 = -2x3