Question

- Найдите корни уравнения:
1) cos2 2х - sin2 2x = 0,5;​

Answer 1

$\cos^{2} (2x) - \sin^{2} (2x) = 0.5 \\ \cos(4x) = \frac{1}{2}$

1 случай:

$4x = \frac{\pi}{3} + 2\pi n \\ x = \frac{\pi}{12} + \frac{\pi n}{2}$

2 случай:

$4x = \frac{5\pi}{3} + 2\pi n \\ x = \frac{5\pi}{12} + \frac{\pi n}{2}$