Question

Решить уравнение: sin 4x - sin 2x = sin 8x

Answer 1

sin8x-sin4x+sin2x=0
2sin2xcos6x+sin2x=0
sin2x(2cos6x+1)=0
sin2x=0⇒2x=πn,n∈z⇒x=πn/2,n∈z
cos6x=-1/2⇒6x=+-2π/3+2πk,k∈z⇒x=+-π/9+πk/3,k∈z