1. Решите уравнения: 2 cosx + √3 = 0; √2-2cosx = 0; √3+2sinx = 0; 1-2sinx=0; 2sinx + √3 = 0; 2 cos x + √2 = 0;

Решение:

1. \( 2 \cos x + \sqrt{3} = 0 \)



\( \cos x = -\frac{\sqrt{3}}{2} \)




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



2. \( \sqrt{2} - 2 \cos x = 0 \)



\( \cos x = \frac{\sqrt{2}}{2} \)




\( x = \pm \frac{\pi}{4} + 2\pi k, k \in \mathbb{Z} \)



3. \( \sqrt{3} + 2 \sin x = 0 \)



\( \sin x = -\frac{\sqrt{3}}{2} \)




\( x = -\frac{\pi}{3} + 2\pi k \text{ или } x = \frac{4\pi}{3} + 2\pi k, k \in \mathbb{Z} \)



4. \( 1 - 2 \sin x = 0 \)



\( \sin x = \frac{1}{2} \)




\( x = \frac{\pi}{6} + 2\pi k \text{ или } x = \frac{5\pi}{6} + 2\pi k, k \in \mathbb{Z} \)



5. \( 2 \sin x + \sqrt{3} = 0 \)



\( \sin x = -\frac{\sqrt{3}}{2} \)




\( x = -\frac{\pi}{3} + 2\pi k \text{ или } x = \frac{4\pi}{3} + 2\pi k, k \in \mathbb{Z} \)



6. \( 2 \cos x + \sqrt{2} = 0 \)



\( \cos x = -\frac{\sqrt{2}}{2} \)




\( x = \pm \frac{3\pi}{4} + 2\pi k, k \in \mathbb{Z} \)

Ответ: 1. \( x = \pm \frac{5\pi}{6} + 2\pi k \); 2. \( x = \pm \frac{\pi}{4} + 2\pi k \); 3. \( x = -\frac{\pi}{3} + 2\pi k \text{ или } x = \frac{4\pi}{3} + 2\pi k \); 4. \( x = \frac{\pi}{6} + 2\pi k \text{ или } x = \frac{5\pi}{6} + 2\pi k \); 5. \( x = -\frac{\pi}{3} + 2\pi k \text{ или } x = \frac{4\pi}{3} + 2\pi k \); 6. \( x = \pm \frac{3\pi}{4} + 2\pi k \), где \( k \in \mathbb{Z} \).