sin6x*sin2x=sin5x*sin3x

Question

sin6x*sin2x=sin5x*sin3x

Answer 1

cos(4x)-cos(8x)=cos2x-cos8x

cos4x=cos2x

2cos^2x-1-cos2x=0

cos2x=t

2t^2-t-1=0

t=-1/2

t=1

cos2x=1

x=Пk

2x=(П+-П/3)+2Пk

x=П/2+-П/6+Пk