Solve the following equation:

$$
5(1-\cos x)=4 \sin x
$$

(From Mr. Imre Kövi, a teacher at Főgymnasium, Igló).
$$
5 \cdot 2 \sin ^{2} \frac{x}{2}=8 \sin \frac{x}{2} \cos \frac{x}{2}
$$

The equation is satisfied if

$$
\sin \frac{x}{2}=0, \text { so } x_{1}=0 \text {. }
$$

Dividing both sides of the equation (1) by $\sin \frac{x}{2}$:

$$
10 \sin \frac{x}{2}=8 \cos \frac{x}{2}
$$

from which

$$
\tan \frac{x}{2}=0.8 \text { and } x_{2}=77^{\circ} 19^{\prime} 10^{\prime \prime}
$$

The problem was solved by:

Feuer Mór, Friedmann Bernát, Galter János, Goldstein Zsigmond, Goldziher Károly, Grünhut Béla, Hofbauer Ervin, Kántor Nándor, Schneider Béla, Szabó István.