### 3.482 Find the maximum value of the expression

$$
A=\frac{\cos 2 \alpha+1}{\operatorname{ctg} \frac{\alpha}{2}-\operatorname{tg} \frac{\alpha}{2}} \text { for } 0<\alpha<\frac{\pi}{2}
$$
Solution. This problem is analogous to problem 3.481.

Answer: $\frac{1}{2}$ when $\alpha=\frac{\pi}{4}$.