داریم: $A={{\operatorname{Cos}}^{2}}{{105}^{{}^\circ }}-{{\operatorname{Cos}}^{2}}{{15}^{{}^\circ }}={{\operatorname{Cos}}^{2}}({{90}^{{}^\circ }}+{{15}^{{}^\circ }})-{{\operatorname{Cos}}^{2}}{{15}^{{}^\circ }}={{(-\sin {{15}^{{}^\circ }})}^{2}}-{{\operatorname{Cos}}^{2}}{{15}^{{}^\circ }}={{\sin }^{2}}{{15}^{{}^\circ }}-{{\operatorname{Cos}}^{2}}{{15}^{{}^\circ }}$ $=-({{\operatorname{Cos}}^{2}}{{15}^{{}^\circ }}-{{\sin }^{2}}{{15}^{{}^\circ }})=-\operatorname{Cos}(2\times {{15}^{{}^\circ }})=-\operatorname{Cos}{{30}^{{}^\circ }}=-\frac{\sqrt{3}}{2}$