A) \[\cos \theta -i\sin \theta \]
B) \[\sin \theta -i\cos \theta \]
C) \[\cos 9\theta -i\sin 9\theta \]
D) \[\sin 9\theta -i\cos 9\theta \]
E) \[\cos \theta +i\sin \theta \]
Correct Answer: D
Solution :
\[\frac{{{(\cos \theta +i\sin \theta )}^{4}}}{{{(\sin \theta +i\cos \theta )}^{5}}}=\frac{{{(\cos \theta +i\sin \theta )}^{4}}}{{{i}^{5}}{{(\cos \theta -i\sin \theta )}^{5}}}\] \[=-i{{(\cos \theta +i\sin \theta )}^{4}}{{(\cos \theta +i\sin \theta )}^{5}}\] \[=-i(\cos 9\theta +i\sin 9\theta )\] \[=\sin 9\theta +i\cos 9\theta \]
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