수학2_삼각함수_삼각함수 덧셈정리_난이도 중

${\dfrac{\sin \theta}{\sin \theta \sin 2\theta}} +{\dfrac{\sin \theta}{\sin 2\theta \sin 3\theta}}+ \cdots +{\dfrac{\sin \theta}{\sin 99\theta \sin 100\theta}}$ 를 간단히 하면?

① $\tan \theta - \tan \theta \cos \theta$          ② $\cot \theta - \cot 100 \theta$

③ $\sin \theta - \sin 100\theta$              ④ $\cos \theta \left ( \cot \theta - \cot 100 \theta \right )$      

⑤ $\tan \theta \left ( \sin \theta - \sin 100 \theta \right )$

정답 ②