1-4 Решите уравнения a) ctg x + √3 = 0; 6) 2 cos 8x = √3; B) 2sin(x/2 - π/6) = -1.

a) ctg x + √3 = 0

ctg x = -√3

$$x = arсtg(-√3) + πn, n \in Z$$

$$x = -\frac{π}{6} + πn, n \in Z$$

Ответ: $$x = -\frac{π}{6} + πn, n \in Z$$

б) 2 cos 3x = √3

cos 3x = √3 / 2

$$3x = ± arccos(\frac{\sqrt{3}}{2}) + 2πn, n \in Z$$

$$3x = ± \frac{π}{6} + 2πn, n \in Z$$

$$x = ± \frac{π}{18} + \frac{2πn}{3}, n \in Z$$

Ответ: $$x = ± \frac{π}{18} + \frac{2πn}{3}, n \in Z$$

в) 2sin(x/2 - π/6) = -1

sin(x/2 - π/6) = -1/2

$$\frac{x}{2} - \frac{π}{6} = arcsin(-\frac{1}{2}) + 2πn, n \in Z$$

$$\frac{x}{2} - \frac{π}{6} = -\frac{π}{6} + 2πn, n \in Z$$

$$\frac{x}{2} = 2πn, n \in Z$$

$$x = 4πn, n \in Z$$

Или

$$\frac{x}{2} - \frac{π}{6} = π - arcsin(-\frac{1}{2}) + 2πn, n \in Z$$

$$\frac{x}{2} - \frac{π}{6} = π - (-\frac{π}{6}) + 2πn, n \in Z$$

$$\frac{x}{2} - \frac{π}{6} = π + \frac{π}{6} + 2πn, n \in Z$$

$$\frac{x}{2} = \frac{7π}{6} + 2πn, n \in Z$$

$$x = \frac{7π}{3} + 4πn, n \in Z$$

Ответ: $$x = 4πn, n \in Z$$ или $$x = \frac{7π}{3} + 4πn, n \in Z$$