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# Solution: What relation can you draw from the given series?

#### Problem Statement: EE Board March 1998

Given the following series:

Sin x = x โ (x^3/3!) + (x^5/5!) + โฆ..

Cos x = 1 โ (x^2/2!) + (x^4/4!) + โฆ..

ex = 1 + x + (x^2/2!) + (x^3/3!) + โฆ.

What relation can you draw from these series?

• A. ex = cos x + sin x
• B. eix = cos x + isin x
• C. eix = icos x + sin x
• D. iex = icos x + isin x

The equivalent relation of the given series is B. eix = cos x + isin x.

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