Statement 1: The system of linear equations x+( sin α) y+( cos α) z=0; x+( cos α) y+( sin α) z=0; x-( sin α) y-( cos α) z=0 has a non-trivial…

Statement $\displaystyle 1$: The system of linear equations $$\begin{aligned} & x+(\sin \alpha) y+(\cos \alpha) z=0 \\ & x+(\cos \alpha) y+(\sin \alpha) z=0 \\ & x-(\sin \alpha) y-(\cos \alpha) z=0 \end{aligned} $$ has a non-trivial solution for only one value of $\displaystyle \alpha$ lying in the interval ( $\displaystyle 0, \pi / 2$ ).Statement $\displaystyle 2$ : The equation in $\displaystyle \alpha$ $$\left|\begin{array}{ccc} \cos \alpha & \sin \alpha & \cos \alpha \\ \sin \alpha & \cos \alpha & \sin \alpha \\ \cos \alpha & -\sin \alpha & -\cos \alpha \end{array} \right\rvert\,=0 $$ has only one solution lying in the interval $\displaystyle (0, \pi / 2)$.