0354. a) cos(-2x)=-1; 6) tg =-1;

354. a) Решим уравнение $$\cos\left(\frac{\pi}{6} - 2x\right) = -1$$.

$$\frac{\pi}{6} - 2x = \arccos (-1) + 2\pi k, k \in \mathbb{Z}$$

$$\frac{\pi}{6} - 2x = \pi + 2\pi k, k \in \mathbb{Z}$$

$$- 2x = \pi - \frac{\pi}{6} + 2\pi k, k \in \mathbb{Z}$$

$$- 2x = \frac{5\pi}{6} + 2\pi k, k \in \mathbb{Z}$$

$$x = -\frac{5\pi}{12} - \pi k, k \in \mathbb{Z}$$

$$x = -\frac{5\pi}{12} + \pi n, n \in \mathbb{Z}$$

Ответ: $$x = -\frac{5\pi}{12} + \pi n, n \in \mathbb{Z}$$

354. б) Решим уравнение $$\operatorname{tg}\left(\frac{\pi}{4} - \frac{x}{2}\right) = -1$$.

$$\frac{\pi}{4} - \frac{x}{2} = \operatorname{arctg} (-1) + \pi k, k \in \mathbb{Z}$$

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

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

$$- \frac{x}{2} = -\frac{\pi}{2} + \pi k, k \in \mathbb{Z}$$

$$x = \pi - 2\pi k, k \in \mathbb{Z}$$

$$x = \pi + 2\pi n, n \in \mathbb{Z}$$

Ответ: $$x = \pi + 2\pi n, n \in \mathbb{Z}$$