Solve for $\theta$ in the range $0° \leq \theta \leq 360°$: $2\cos^2\theta - \cos\theta - 1 = 0$.
A60°, 180°, 300°
B0°, 120°, 240°CORRECT
C90°, 270°, 360°
D30°, 150°, 270°
GCEFurther MathematicsTrigonometry and Circular Measure2023
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Factorising 2cos²θ − cos θ − 1 = 0 gives (2cos θ + 1)(cos θ − 1) = 0. So cos θ = −1/2 or cos θ = 1. cos θ = 1 gives θ = 0° (and 360°, same point); cos θ = −1/2 gives θ = 120° and 240°. The solutions in [0°, 360°] are 0°, 120°, 240°.
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