Решите уравнение sin(x - (pi)/(3)) - cos(x + (pi)/(6)) = sin(x + (pi)/(3)) + cos(x - (pi)/(6)) + sqrt(3) .

sin(x - (pi)/(3)) - cos(x + (pi)/(6)) = sin(x + (pi)/(3)) + cos(x - (pi)/(6)) + sqrt(3) 2sin(x - (pi)/(3)) = 2sin(x + (pi)/(3)) + sqrt(3) 4cos x sin(pi)/(3) = -sqrt(3) cos x = -1/2 x = +- 2pi/3 + 2kpi, k in Z.

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