Answer:
x = 0, π/3, π/2, 2π/3, π, 4π/3, 3π/2, 5π/3
Step-by-step explanation:
sin(2x) + sin(4x) = 0
Use double angle formula.
sin(2x) + 2 sin(2x) cos(2x) = 0
Factor.
sin(2x) (1 + 2 cos(2x)) = 0
Solve.
sin(2x) = 0, cos(2x) = -½
2x = 0, 2π/3, π, 4π/3, 2π, 8π/3, 3π, 10π/3
x = 0, π/3, π/2, 2π/3, π, 4π/3, 3π/2, 5π/3
