The Fourier series of a periodic function f(x) is given by 6+ cos(nz) + sin(nz). 6" n-1 The best approximation of f by a Fourier polynomial (or trigonometric polynomial) of degree 2 is 1 1) F(x) = cos z + 2 sinx+ cos(22) + sin(2r). 64 36 2) F(z) = 36 cos(2z) + sin(2z). 64 1 3) F(z) = 6+ 1 2 sin z + 36 cos(2z) -sin(2z). 6COS 64 1 4) F(x)= 6+ cos z +2 sin z+ 1 cos(2z) + sin(2x).

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A: Given,

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