1. Find the value of $\cos ^{2} 73^{\circ}+\cos ^{2} 47^{\circ}+\cos 47^{\circ} \cos 43^{\circ}$. (1987, Jiangsu Youth Mathematics Summer Camp)
$\begin{array}{l}\text { 1. Let } F=\cos ^{2} 73^{\circ}+\cos ^{2} 47^{\circ}+\cos 47^{\circ} \cdot \cos 73^{\circ}, F^{\prime} \\ \text {- } \sin ^{2} 73^{\circ}+\sin ^{2} 47^{\circ}-\sin 47^{\circ} \sin 73^{\circ} \text {. Then } F+F^{\prime}=2 \text { , } \\ \cos 120^{\circ}=\frac{3}{2}, F-F^{\prime}=2 \cos 120^{\circ} \cos 26^{\circ}+\cos 26^{\circ}=0 \text {. } \\ \text { Therefore, } F=\frac{3}{4} \text {. }\end{array}$