4.3. In a triangle $A B C$ the following relation holds:

$$
\sin ^{23} \frac{\alpha}{2} \cdot \cos ^{48} \frac{\beta}{2}=\sin ^{23} \frac{\beta}{2} \cdot \cos ^{48} \frac{\alpha}{2}
$$

where $\alpha$ and $\beta$ are the corresponding angles at $A$ and $B$. Find the ratio $A C / B C$.

(Cyprus)
4.3. For every $s$ and $t$ such that $0\cos ^{48} t$. Therefore the function

$$
f(t)=\frac{\sin ^{23} t}{\cos ^{48} t}
$$

is strictly increasing on $(0, \pi / 2)$. So from $f(\alpha / 2)=f(\beta / 2)$ we get $\alpha=\beta$, that is $A C / B C=1$.

## Figure 4.4.