حاصل عبارت $\frac{\sin {{۳۰}^{\circ }}\cos {{۶۰}^{\circ }}-\sin {{۶۰}^{\circ }}\cos {{۳۰}^{\circ }}}{{{\tan }^{۲}}{{۴۵}^{\circ }}-\tan {{۶۰}^{\circ }}}$ کدام است؟
$\begin{align} & \overset{\Delta }{\mathop{AHC}}\,:\left\{ \begin{matrix} \cos {{30}^{\circ }}=\frac{CH}{AC}\Rightarrow CH=\frac{\sqrt{3}}{2}AC=\frac{\sqrt{3}}{2}\times 6=3\sqrt{3} \\ \sin {{30}^{\circ }}=\frac{AH}{AC}\Rightarrow AH=\frac{1}{2}AC=\frac{1}{2}\times 6=3 \\\end{matrix} \right. \\ & \overset{\Delta }{\mathop{ABH}}\,:B{{H}^{2}}=A{{B}^{2}}-A{{H}^{2}}={{5}^{2}}-{{3}^{2}}=16\Rightarrow BH=4 \\ & \Rightarrow BC=BH+CH=4+3\sqrt{3} \\ \end{align}$