The Fourier cosine series of an even function is f(x)=a 0+ n=1a n(nx). For f(x)=2x on [0,], find a 2.

GATE 2018 ME (ME2) – Question 11

The Fourier cosine series of an even function is $f(x)=a_0+\sum_{n=1}^{\infty}a_n\cos(nx)$. For $f(x)=\cos^2x$ on $[0,\pi]$, find $a_2$.

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Correct answer: (C) 0.5

Use $\cos^2x=(1+\cos2x)/2$. Comparing with the specified cosine series gives $a_0=1/2$, $a_2=1/2$ and all other coefficients zero. Answer **0.5, C**.