Answer:
π/3, π, 5π/3
Step-by-step explanation:
Remember that: sin 2x = 2 sin x cos x. (Double-Angle Identity)
Given: sin 2x = sin x
Then, sin 2x - sin x = 0
2 sin x cos x - sin x = 0
sin x (2 cos x - 1) = 0
Case 1: sin x = 0
x = 0, π, 2π
However, it is given that x must satisfy 0 < x < 2π which means that only π satisfies this condition.
Case 2: 2 cos x - 1 = 0
2 cos x = 1
cos x = 1/2
x = π/3, 5π/3
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~~DeanGD20
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