8.094. $\frac{1-\cos x}{\sin \frac{x}{2}}=2$.
## Solution.

Domain of definition: $\sin \frac{x}{2} \neq 0$.

From the condition

$$
\begin{aligned}
& \frac{1-\cos 2\left(\frac{x}{2}\right)}{\sin \frac{x}{2}}=2 \Leftrightarrow \frac{1-1+2 \sin ^{2} \frac{x}{2}}{\sin \frac{x}{2}}=2 \Rightarrow \sin \frac{x}{2}=1, \frac{x}{2}=\frac{\pi}{2}+2 \pi k \\
& x=\pi+4 \pi k=\pi(4 k+1), k \in \mathbb{Z}
\end{aligned}
$$

Answer: $\quad x=\pi(4 k+1), k \in \mathbb{Z}$.