TN SET 2017 Questions & Answers

TN SET 2017 MATHS QUESTION.
Real part of exp (exp ix) is
1.e^ cos x
2. e^ cos x. (cos (cos x))
3. e^ cos x. (sin (cos x))
4. e^ cos x. (cos (sin x))

Answer:
WKT e^i x = cos x + i sin x.
So
e ^ e^i x = e ^ ( cos x + i sin x)
= e^ cos x .e^ i sin x
= e^ cos x . {cos (sin x)+ i sin (sin x)}
Real part is
e^ cos x . cos (sin x).
Ans (4)

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