8.174. $\operatorname{tg}^{2} 3 x-2 \sin ^{2} 3 x=0$.

8.174. $\tan^{2} 3 x-2 \sin ^{2} 3 x=0$.
## Solution.

Domain of definition: $\cos 3 x \neq 0$.

We have $\frac{\sin ^{2} 3 x}{\cos ^{2} 3 x}-2 \sin ^{2} 3 x=0, \sin ^{2} 3 x \cdot\left(\frac{1}{\cos ^{2} 3 x}-2\right)=0$.

From this:

1) $\sin 3 x=0, \quad 3 x=\pi k, \quad x_{1}=\frac{\pi k}{3}, k \in Z$;
2) $\frac{1}{\cos ^{2} 3 x}-2=0, \cos 3 x= \pm \frac{\sqrt{2}}{2}, \quad 3 x=\frac{\pi}{4}+\frac{\pi n}{2}, \quad x_{2}=\frac{\pi}{12}+\frac{\pi n}{2}=$ $=\frac{\pi}{12}(2 n+1), n \in Z$.

Answer: $\quad x_{1}=\frac{\pi k}{3} ; x_{2}=\frac{\pi}{12}(2 n+1) \quad k, n \in Z$.