question_answer

If\[n\in N\],then \[\sin \theta +\sin 2\theta +\sin 3\theta +....+\sin n\theta =\]

A)  \[\sin \left[ \frac{n(n+1)\theta }{2} \right]\]

B)  \[\frac{\sin \left[ \frac{(n+1)}{2}\theta  \right]\sin \theta }{\sin \left( \frac{\theta }{2} \right)}\]

C)  \[\frac{\sin \left[ \frac{(n+1)}{2}\theta  \right]\sin \left( \frac{n\theta }{2} \right)}{\sin \left( \frac{\theta }{2} \right)}\]

D)  \[\frac{\sin \left[ \frac{(n+1)}{2}\theta  \right]{{\sin }^{n}}\left( \frac{\theta }{2} \right)}{\sin \left( \frac{\theta }{2} \right)}\]