If maximum and minimum values of the determinant $\left|\begin{array}{l}1+Si{n}^{2}xCo{s}^{2}xSin2x\\ Si{n}^{2}x1+Co{s}^{2}xSin2x\\ Si{n}^{2}xCo{s}^{2}x1+Sin2x\end{array}\right|$ are $\alpha and\beta$ respectively , then which of the statements are FALSE ?

$\left|\begin{array}{l}1+{\sin }^{2}xCo{s}^{2}xSin2x\\ Si{n}^{2}x1+Co{s}^{2}xSin2x\\ Si{n}^{2}xCo{s}^{2}x1+Sin2x\end{array}\right|=\left|\begin{array}{l}1+Si{n}^{2}xCo{s}^{2}xSin2x\\ -110\\ 0-11\end{array}\right|$

$\begin{array}{l}=(1+Si{n}^{2}x)(1+0)-Co{s}^{2}x(-1-0)+Sin2x(1-0)\\ =2+Sin2x\\ \Rightarrow \alpha =2+1=3,\beta =2-1=1\end{array}$

A triangle can be constructed having its sides as $\alpha =3,\beta =1$and $\alpha -\beta =2$ is false