sinx+sin2x+sin3x+sin4x=0 помогите плиз

Question

sinx+sin2x+sin3x+sin4x=0 помогите плиз

Answer 1

2sin2xcosx+2sin3xcosx=0

cos(sin2x+sin3x)=0

cosx2sin5/2x*cosx/2=0

sin5x/2*cosx/2*cosx=0

sin5x/2=0, cosx/2=0, cosx=0

5x/2=пn, x/2=п/2+пm, x=п/2+пk

x=5/2пn, x=п+2пm, x=п/2+пk

Ответ: x=п/2y, x=2/5пs