Решить уравнение sin 2x + sin x = 0

sin 2x + sin x = 0

2sinxcosx+sinx=0

sinx=0

x=pin

2cosx+1=0

cosx=-0,5

x=+-2pi/3+2pin,  n є Z

sin 2x = 2sin x cos x

С учётом этого перепишем уравнение в таком виде:

2 sin x cos x + sin x = 0

sin x(2cos x + 1) = 0

sin x = 0                        или                  2cos x + 1 = 0

x = πn,n∈Z                                              2cos x = -1

                                                                    cos x = -1/2

                                                                    x = ±arccos(-1/2) + 2πk,k∈Z

                                                                   x = ±2π/3 + 2πk,k∈Z