Cos(2x +2π/3) = Cos2(x +π/3) = 1 - 2Sin²(x +π/3)
Cos(2x+2π/3)+4Sin(x+π/3)=5/2,
1 - 2Sin²(x +π/3)+4Sin(x+π/3)=5/2,
Sin(x+π/3)=t,
-2t² + 4t-1,5 = 0
4t² -8t +3 = 0
t = (4+-√(16 -12)/4
t₁ =6/4 = 1,5 t₂=0,5
Sin(x + π/3) = 1,5 Sin(x+π/3)=0,5,
∅ x + π/3 = (-1)^n arcSin0,5 + nπ, n ∈Z
x + π/3 = (-1)^n* π/6 + nπ, n ∈ Z
x = -π/3 = (-1)^n* π/6 + nπ, n ∈ Z