54 Решить уравнение: 1) sin (5π + x) = 1; 3) cos(x+x) = -1; 2 2) cos (x + 3π) = 0; 4) sin(9π + x) = -1.

1) \( \sin(5\pi + x) = 1 \) \( \sin(\pi + x) = 1 \) \( \pi + x = \frac{\pi}{2} + 2\pi n, n \in Z \) \( x = -\frac{\pi}{2} + 2\pi n, n \in Z \) 2) \( \cos(x + 3\pi) = 0 \) \( \cos(x + \pi) = 0 \) \( x + \pi = \frac{\pi}{2} + \pi n, n \in Z \) \( x = -\frac{\pi}{2} + \pi n, n \in Z \) 3) \( \cos(\frac{9}{2}\pi + x) = -1 \) \( \cos(\frac{\pi}{2} + x) = -1 \) \( \frac{\pi}{2} + x = \pi + 2\pi n, n \in Z \) \( x = \frac{\pi}{2} + 2\pi n, n \in Z \) 4) \( \sin(\frac{9}{2}\pi + x) = -1 \) \( \sin(\frac{\pi}{2} + x) = -1 \) \( \frac{\pi}{2} + x = -\frac{\pi}{2} + 2\pi n, n \in Z \) \( x = -\pi + 2\pi n, n \in Z \) Ответ: 1) x = -π/2 + 2πn, n ∈ Z; 2) x = -π/2 + πn, n ∈ Z; 3) x = π/2 + 2πn, n ∈ Z; 4) x = -π + 2πn, n ∈ Z.