$The expression of trigonometric Fourier series co-efficient a_{n} in terms of exponential Fourier series co-efficient C_{n} is$

C_{n} - C_{- n}

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C_{n} + C_{- n}

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j (C_{n} - C_{- n})

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j (C_{n} + C_{- n})

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Solution

The correct option is B $C_{n} + C_{- n}$
Ans : (c)

$we know that, a_{n} = \frac{2}{T} \int_{T} x (t) c o s (ω_{0} n t) d t = \frac{2}{T} \int_{T} x (t) [\frac{e^{j ω_{0} n t} + e^{- j ω_{0} n t}}{2}] d t = \frac{1}{T} [\int_{T} x (t) e^{j ω_{0} n t} d t + \int_{T} x (t) e^{- j ω_{0} n t} d t] a_{n} = C_{n} + C_{- n} [By the definition of exponential Fourier series co-efficient]$

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