Question

Real part of $e^{e^{i\theta }}$ is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$e^{e^{i\theta }}=e^{cos\theta +isin\theta }=e^{cos\theta }{e}^{isin\theta }=e^{cos\theta }\left[cos\right(sin\theta )+isin(sin\theta \left)\right]\therefore Realpartof{e}^{e^{i\theta }}is{e}^{cos\theta }\left[cos\right(sin\theta \left)\right]$