2.3. sin(1/2 x - 5π/6) = √3/2;

Решим уравнение:

$$sin(\frac{1}{2}x - \frac{5\pi}{6}) = \frac{\sqrt{3}}{2}$$

\(\frac{1}{2}x - \frac{5\pi}{6} = arcsin(\frac{\sqrt{3}}{2})\)

\(\frac{1}{2}x - \frac{5\pi}{6} = \frac{\pi}{3} + 2\pi k, k \in Z\)

\(\frac{1}{2}x = \frac{\pi}{3} + \frac{5\pi}{6} + 2\pi k, k \in Z\)

\(\frac{1}{2}x = \frac{7\pi}{6} + 2\pi k, k \in Z\)

$$x = \frac{7\pi}{3} + 4\pi k, k \in Z$$

или

\(\frac{1}{2}x - \frac{5\pi}{6} = \pi - \frac{\pi}{3} + 2\pi k, k \in Z\)

\(\frac{1}{2}x = \frac{2\pi}{3} + \frac{5\pi}{6} + 2\pi k, k \in Z\)

\(\frac{1}{2}x = \frac{9\pi}{6} + 2\pi k, k \in Z\)

\(\frac{1}{2}x = \frac{3\pi}{2} + 2\pi k, k \in Z\)

$$x = 3\pi + 4\pi k, k \in Z$$

Ответ: $$x = \frac{7\pi}{3} + 4\pi k, k \in Z$$ или $$x = 3\pi + 4\pi k, k \in Z$$