Решите уравнение sin^4 x + sin( x + (pi)/(3) ) sin( x - (pi)/(3) ) = 0 .

sin^4 x + sin( x + (pi)/(3) ) sin( x - (pi)/(3) ) = 0 sin^4 x + (1)/(2)( cos(2pi)/(3) - cos 2x ) = 0 4sin^4 x - 1 - 2cos 2x = 0 4sin^4 x + 4sin^2 x - 3 = 0 (2sin^2 x - 1)(2sin^2 x + 3) = 0 sin x = +-(1)/(sqrt(2)) x = pi/4 + kpi/2, k in Z.

x = \pi/4 + k\pi/2,\ k \in \mathbb{Z}