Let \( z=\cos \theta+i \sin \theta \), where \( i=\sqrt{-1} \). The...
Let \( z=\cos \theta+i \sin \theta \), where \( i=\sqrt{-1} \). Then the value of \( \sum_{m=1}^{15} \operatorname{Im}\left(z^{2 m-1}\right) \) at \( \theta=2^{\circ} \) is
\( \mathrm{P} \)
W
(a) \( \frac{1}{\sin 2^{\circ}} \)
(b) \( \frac{1}{3 \sin 2^{\circ}} \)
[IIT-JEE 2009, 3M]
(c) \( \frac{1}{2 \sin 2^{\circ}} \)
(d) \( \frac{1}{4 \sin 2^{\circ}} \)
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