If \( \theta \in R \) and \( i=\sqrt{-1} \), then \( \left(\frac{1+\sin \theta+i \cos \theta}{1+...
If \( \theta \in R \) and \( i=\sqrt{-1} \), then \( \left(\frac{1+\sin \theta+i \cos \theta}{1+\sin \theta-i \cos \theta}\right)^{n} \) is equal to
(a) \( \cos \left(\frac{n \pi}{2}-n \theta\right)+i \sin \left(\frac{n \pi}{2}-n \theta\right) \)
(b) \( \cos \left(\frac{n \pi}{2}+n \theta\right)+i \sin \left(\frac{n \pi}{2}+n \theta\right) \)
(c) \( \sin \left(\frac{n \pi}{2}-n \theta\right)+i \cos \left(\frac{n \pi}{2}-n \theta\right) \)
(d) \( \cos \left(n\left(\frac{\pi}{2}+2 \theta\right)\right)+i \sin \left(n\left(\frac{\pi}{2}+2 \theta\right)\right) \)
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