Alll possible values of x such that Sin (2x) = sin (x) and 0 ≤ x ≥ 2π are; 0, π/3, 2π, π, 5π/3
We are given that;
Sin (2x) = sin (x) and 0 ≤ x ≥ 2π
Now, all the possible values of x can be determined by using trigonometry properties.
Now, According to trigonometry properties:
If sin θ = sin α, then;
θ = α + 2Kπ or θ = π - α + 2Kπ
This means that Sin (2x) = sin (x) will be expressed as;
2x = x + 2Kπ or 2x = π - x + 2Kπ
Thus, simplifying that gives;
x = 2Kπ or 3x = π(1 + 2K)
That is general solution, the question wants us to get the value of x between 0 and 2π. Thus;
At k = 0, x = 0 or π/3
At k = 1, x = 2π or π
At k = 2, x = 5π/3
Read more about trigonometric properties at; https://brainly.com/question/5093486
