Решить уравнение:

(sin12x) / (sin8x) = (cos6x) / (cos2x)

(sin12x) / (sin8x) = (cos6x) / (cos2x)

sin8x≠0 U cos2x≠0

8x≠πn⇒x≠πn/8 U 2x≠π/2+πn⇒x≠π/4+πn/2

sin12x*cos2x=cos6x*sin8x

1/2[sin6x+sin14x]=1/2[sin2x+sin14x]

sin6x+sin14x-sin2x-sin14x=0

sin6x-sin2x=0

2sin2xcos4x=0

sin2x=0⇒2x=πn⇒x=πn/2

cos4x=0⇒4x=π/2+πn⇒x=π/8+πn/4