삼각방정식 실근 개수

$\cos ^{2} x - \sin ^{2} 2 x = 0$$( 0 \leq x \leq 2 \pi )$에서 $\rightarrow \cos ^{2} x - 4 \sin ^{2} x \cos ^{2} x = 0$ $\rightarrow \cos ^{2} x ( 1 - 4 \sin ^{2} x ) = 0$ $\displaystyle \cos x = 0 \text{또는} \sin ^{2} x = \frac{1}{4}$ $\displaystyle \therefore x = \frac{\pi}{2} , \frac{3}{2} \pi$ 또는 $\displaystyle x = \frac{\pi}{6} , \frac{5}{6} \pi , \frac{7}{6} \pi , \frac{11}{6} \pi$ ∴ 모두 $6$개