$\sin ^{2} 30^{\circ}+\operatorname{tg} 30^{\circ} \operatorname{tg} 120^{\circ}+\sin ^{2} 120^{\circ}=?$


$$
\begin{gathered}
\sin ^{2} 30^{\circ}+\operatorname{tg} 30^{\circ} \operatorname{tg} 120^{\circ}+\sin ^{2} 60^{\circ}=\sin ^{2} 30^{\circ}+\cos ^{2} 30^{\circ}-\operatorname{tg} 30^{\circ} \operatorname{tg} 60^{\circ}= \\
=1-\operatorname{tg} 30^{\circ} \operatorname{ctg} 30^{\circ}=1-1=0 .
\end{gathered}
$$

(Steinitz Károly, Pécs.)

