Cos2x+cos5x+cosx=0 решите плиз

Question

Cos2x+cos5x+cosx=0
решите плиз

Answer 1

Cos2x+(cos5x+cosx)=cos2x+2cos[(5x+x)/2]*cos[(5x-x)/2]=
=cos2x+2cos3x*cos2x=cos2x*(1+2cos3x)
cos2x(1+2cos3x)=0
cos2x=0⇒2x=π/2+πk⇒x=π/4+πk/2,k∈z
cos3x=-1/2⇒3x=+-π/3+2πk⇒x=+-π/9+2πk/3,k∈z