WAEC Further Mathematics 2015 Paper

$2\sin^{2}\theta = 1 + \cos\theta$

$2 ( 1 - \cos^{2}\theta) = 1 + \cos\theta$

$2 - 2\cos^{2}\theta = 1 + \cos\theta$

$0 = 1 - 2 + \cos\theta + 2\cos^{2}\theta$

$2\cos^{2}\theta + \cos\theta - 1 = 0$

Factorizing, we have

$(\cos\theta + 1)(2\cos\theta - 1) = 0$

Note: In the range, $0^{\circ} \leq \theta \leq 90^{\circ}$, all trig functions are positive, so we consider

$2\cos\theta = 1 \implies \cos\theta = \frac{1}{2}$

$\theta = 60^{\circ}$.