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GATE2018-2-1

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The Fourier cosine series for an even function $f(x)$ is given by $$ f(x)=a_0 + \Sigma_{n=1}^\infty a_n \cos (nx).$$ The value of the coefficient $a_2$ for the function $f(x)=\cos ^2 (x)$ in $[0, \pi]$ is

  1. $-0.5$
  2. $0.0$
  3. $0.5$
  4. $1.0$

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