Решить уравнение: (sin12x)/(sin8x)=(cos6x)/(cos2x)

Question

Решить уравнение:
(sin12x)/(sin8x)=(cos6x)/(cos2x)

Answer 1

(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