삼각함수 성질

[출제의도] 삼각함수의 성질 이해하기 $\displaystyle \sin \left( \frac{\pi}{2} - \theta \right) = \cos \theta$, $\tan \left( \pi + \theta \right) = \tan \theta$이므로 $\displaystyle 2 \sin \left( \frac{\pi}{2} - \theta \right) = \sin \theta \times \tan \left( \pi + \theta \right)$에서 $2 \cos \theta = \sin \theta \times \tan \theta$ $\displaystyle 2 \cos \theta = \sin \theta \times \frac{\sin \theta}{\cos \theta}$ $2 \cos ^{2} \theta = \sin ^{2} \theta$ $\sin ^{2} \theta + \cos ^{2} \theta = 1$이므로 $2 \left( 1 - \sin ^{2} \theta \right) = \sin ^{2} \theta$ 따라서 $\displaystyle \sin ^{2} \theta = \frac{2}{3}$