sinx+sin5x+cosx+cos5x=0

Question

sinx+sin5x+cosx+cos5x=0

Answer 1

2sin3xcos2x+2cos3xcos2x=0

cos2x(sin3x+cos3x)=0

cos2x=0

x=П/4+пk/2

sin3x+cos3x=0

tg3x=-1

3x=-П/4+Пk

x=-П/12+Пk/3

Answer 2

2sin3xcos2x+2cos3xcos2x=0

cos2x(sin3x+cos3x)=0

cos2x=0

x=П/4+пn/2

sin3x+cos3x=0

tg3x=-1

3x=-П/4+Пn

x=-П/12+Пn/3