Let sin(2x) = cos(x), where 0° ≤ x < 180°. What are the possible values for x?

Use the double-angle identity: sin(2x) = 2sin(x)cos(x). Then cos(x)(2sin(x) − 1) = 0, so either cos(x) = 0, giving x = 90°, or sin(x) = 1/2, giving x = 30° or 150° in the stated interval. Thus the possible values are 30°, 90°, or 150°.

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