Real part of e^ e^ i is - Vidyadip

MCQ

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

✓
${e^{\cos \theta }}[\cos (\sin \theta )]$
B
${e^{\cos \theta }}[\cos (\cos \theta )]$
C
${e^{\sin \theta }}[\sin (\cos \theta )]$
D
${e^{\sin \theta }}[\sin (\sin \theta )]$

✓

Answer

Correct option: A.

${e^{\cos \theta }}[\cos (\sin \theta )]$

a
(a)${e^{{e^{i\theta }} = {e^{\cos \theta + i\sin \theta }} = {e^{\cos \theta }}[{e^{i\sin \theta }}]}}$$ = {e^{\cos \theta }}[\cos (\sin \theta ) + i\sin (\sin \theta )]$
Real part of ${e^{{e^{i\theta }}}}$is ${e^{\cos \theta }}[\cos (\sin \theta )]$

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