If Δ _ 1 = | cases x & sinθ & cosθ - sinθ & - x & 1 cosθ & 1 & x...

{\Delta}_{1} = \left|\begin{cases}x & sin\theta \\ - sin\theta & - x \\ cos\theta & 1\end{cases}$$\begin{array}{ll}cos\theta \\ 1 \\ x\end{array}$$\right|$<br />$= x\left(- {x}^{2} - 1\right) - sin\theta\left(- xsin\theta - cos\theta\right) + cos\theta ( - sin\theta + xcos\theta )$<br />$= - {x}^{3} - x + xsi{n}^{2}\theta + sin\theta cos \theta - sin\theta cos\theta + xco{s}^{2}\theta$<br />$= - {x}^{3} - x + x\left(\sin^{2} \theta + \cos^{2} \theta\right)$<br />$= - {x}^{3}$<br />Similarly:${\Delta}_{2} = - {x}^{3}$<br />$∴ {\Delta}_{1} + {\Delta}_{2} = - 2{x}^{3}$