A) \[\cos (\alpha +\beta -\gamma -\delta )-i\,\sin (\alpha +\beta -\gamma -\delta )\]
B) \[\cos (\alpha +\beta -\gamma -\delta )+i\,\sin (\alpha +\beta -\gamma -\delta )\]
C) \[\sin (\alpha +\beta -\gamma -\delta )-i\,\cos (\alpha +\beta -\gamma -\delta )\]
D) \[\sin (\alpha +\beta -\gamma -\delta )+i\,\cos (\alpha +\beta -\gamma -\delta )\]
Correct Answer: B
Solution :
\[\frac{(\cos \alpha +i\sin \alpha )\,\,(\cos \beta +i\sin \beta )}{(\cos \gamma +i\sin \gamma )\,\,(\cos \delta +i\sin \delta )}\] \[=\cos (\alpha +\beta -\gamma -\delta )+i\sin (\alpha +\beta -\gamma -\delta )\] [By de-movire's theorem].
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