8.332. $\operatorname{tg} x \operatorname{tg}(x+1)=1$.

8.332. $\tan x \tan(x+1)=1$.
Solution.

Domain of definition: $\left\{\begin{array}{l}\cos x \neq 0 \\ \cos (x+1) \neq 0\end{array}\right.$

## Write the equation in the form

$\frac{\sin x \sin (x+1)}{\cos x \cos (x+1)}-1=0 \Leftrightarrow \sin x \sin (x+1)-\cos x \cos (x+1)=0 \Leftrightarrow$

$\Leftrightarrow-\cos (2 x+1)=0, 2 x+1=\frac{\pi}{2}+\pi k, x=\frac{\pi}{4}-\frac{1}{2}+\frac{\pi k}{2}, k \in Z$.

Answer: $x=\frac{\pi}{4}-\frac{1}{2}+\frac{\pi k}{2}, k \in Z$