sinx*cos2x*cos4x=1/8

Question

sinx*cos2x*cos4x=1/8

Answer 1

Sinx*cosx*cos2x*cos4x=1/8*cosx
1/2sin2xcos2xcos4x=1/8cosx
1/4sin4xcos4x=1/8cosx
1/8sin8x=1/8cosx
sin8x-cosx=0
sin8x-sin(П/2-x)=0
2sin(4,5x-П/4)cos(3,5x+П/4)=0
9/2x-П/4=Пk  9/2x=П/4+Пk  x=П/18+2Пk/9
П/4+7/2x=П/2+Пk
7/2x=П/4+Пk
x=П/14+2Пk/7