Find the solutions / show steps

Sin2x+sin (4x) = 0

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