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

Use the identity cos(2x) = 2cos²(x) − 1. Setting this equal to cos(x) gives 2cos²(x) − cos(x) − 1 = 0, which factors as (2cos(x) + 1)(cos(x) − 1) = 0. Thus cos(x) = −1/2 or cos(x) = 1; in the interval from 0° to 180°, these occur at x = 120° and x = 0°, respectively. The possible values are 0° or 120°.

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