Question

Решите пожалуйста
sin3x=-1

Answer 1

sin3x = sin(2x + x) = sin2x*cosx + cos2x*sinx = 2sinx*cos^2x + cos2x*sinx
2sinx*cos^2x + cos2x*sinx - sinx = 0
sinx(2cos^2x + cos2x - 1) = 0
sinx = 0; x = pik, k прин Z
2cos^2x + cos2x - 1 = 0
1 + cos2x + cos2x - 1 = 0
2cos2x = 0
cos2x = 0
2x = pi/2 + pik, k прин Z
x = pi/4 + pik/2, k прин Z