Cos (2x+2π/3) + 4sin (x+π/3) = 5/2

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