삼각방정식

$\displaystyle 4 \sin ^{2} x - 4 \cos \left( \frac{\pi}{2} + x \right) - 3 = 0$ $4 \sin ^{2} x + 4 \sin x - 3 = 0$ $( 2 \sin x - 1 ) ( 2 \sin x + 3 ) = 0$ $- 1 \leq \sin x \leq 1$이므로 $\displaystyle \sin x = \frac{1}{2}$ $\displaystyle x = \frac{\pi}{6} , \frac{5}{6} \pi , 2 \pi + \frac{\pi}{6} , 2 \pi + \frac{5}{6} \pi$, 따라서 모든 해의 합은 $6 \pi$