The Fourier cosine series for an even function is given by f(x)=a_{0}+\sum_{n=1}^{\infty} a_{n} \cos (n x) The value of the coefficient a_{2} for the function f(x)=\cos ^{2}(x) in [0, \pi] is

GATE Mechanical Engineering (ME) 2018 Shift 2 Solved Paper

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The Fourier cosine series for an even function is given by

f(x)=a_{0}+∑↙{n=1}↖{∞} a_{n} \cos (n x)

The value of the coefficient

a_{2}

for the function

f(x)=\cos ^{2}(x)

[0, π]

Solution:

\cos ^{2} x=\;{1+\cos 2 x}/{2}

f(x)=\;{1}/{2}+\;{\cos 2 x}/{2}

f(x)=\;{a_{0}}/{2}+∑↙{n=1}↖{∞} a_{n} ⋅ \cos n x

a_{0}=1

a_{1}=0

a_{2}=\;{1}/{2}

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