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