Question

Решить уравнение: 2cos(4x-п/3)=1

Answer 1

Ответ:

$2 \cos(4x - \frac{\pi}{3} ) = 1 \\ \cos(4x - \frac{\pi}{3} ) = \frac{1}{2} \\ \\ 4x - \frac{\pi}{3} = ±arccos \frac{1}{2} + 2\pi \: n,n∈Z \\ 4x = ±( \frac{\pi}{3} - \frac{\pi}{3} ) + 2\pi \: n ,n∈Z \\ 4x = 2\pi \: n,n∈Z \\ x = \frac{\pi \: n}{2},n∈Z$