30°
45°
60°
90°
Correct answer is C
2\sin^{2}\theta = 1 + \cos \theta \implies 2(1 - \cos^{2}\theta) = 1 + \cos \theta
2 - 2\cos^{2}\theta = 1 + \cos \theta
2 - 2\cos^{2}\theta - 1 - \cos \theta = 0
2\cos^{2}\theta + \cos \theta - 1 = 0
2\cos^{2}\theta + 2\cos\theta - \cos \theta - 1 = 0 \implies 2\cos \theta(\cos \theta + 1) - 1(\cos \theta + 1) = 0
(2\cos \theta - 1)(\cos \theta + 1) = 0 \implies \cos \theta = \frac{1}{2}
\theta = \cos^{-1} \frac{1}{2} = 60°
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