Question

cos(2x+2π/3)+4sin(x+π/3)=5/2

Answer 1

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