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Real part of $e^{e^{i \theta}}$ is
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The correct answer is:
$e^{\cos \theta}[\cos (\sin \theta)]$
$e^{e^{i \theta}}=e^{\cos \theta+i \sin \theta}=e^{\cos \theta}\left[e^{i \sin \theta}\right]=e^{\cos \theta}[\cos (\sin \theta)+i \sin (\sin \theta)]$
$\therefore$ Real part of $e^{e^{i \theta}}$ is $e^{\cos \theta}[\cos (\sin \theta)]$
$\therefore$ Real part of $e^{e^{i \theta}}$ is $e^{\cos \theta}[\cos (\sin \theta)]$
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