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Find all values of x such that sin 2x = sin x at 0 < x < 21π​

Sagot :

DeanGD20idn

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

Please mark me brainliest if it helps!

~~DeanGD20

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