ПОМОГИТЕЕЕ!!! cos x * cos3x= -1/2
Cosx*cos3x=1/2(cos4x+cos2x) ⇒ cos4x+cos2x=-1 2cos²2x-1+cos2x+1=0 t=cos2x ⇒ 2t²+t=0 t(2t+1)=0 t₁=0 t₂=-1/2 cos2x=0 2x=π/2+2πn x=π/4+πn, n∈Z cos2x=-1/2 2x=±arccos(-1/2)+2πk 2x=±2π/3+2πk x=±π/3+πk, k∈Z