Найдите сумму корней уравнения 1-sin5x = (cos3x/2-sin3x/2) ^2 принадлежащих их отрезку [360 градусов; 450 град.]

1 - sin5x = (cos 3x/2 - sin 3x/2) ^2 1 - sin5x = cos^2 3x/2 - 2cos 3x/2 * sin 3x/2 + sin^2 3x/2 1 - sin5x = 1 - 2cos 3x/2 * sin 3x/2 1 - sin5x = 1 - sin3x - sin5x + sin3x = 1 - 1 sin5x - sin3x = 0 2sin (5x - 3x) / 2 * cos (5x + 3x) / 2 = 0 2sinx * cos4x = 0 sinx = 0 x = pin cos4x = 0 x = pi/8 + pin/4 [360 гр; 450 гр] = [2pi; 2,5pi] pin = > n = 2 2pi pi/8 + pin/4 = > n = 8 17pi/8 n = 9 19pi/8 2pi + 17pi/8 + 19pi/8 = 2pi + 36pi/8 = 2pi + 4,5pi = 6,5pi Ответ: 6,5pi