Find the trigonometric Fourier series for the function f(x): [-π/2, π/2] → R given by the expression: f(x) = ²/2/² FS(x) = FS(x)= FS(x) sinh a 75 = O FS(z) =sinh7|1+2% (-1) (cos 2n +nsin 2ng) ] e)]. sinh a 71 2 sin T T [12 + Σn=1 n²+1 (-1)" (cos 2nx √2+ (-1)" + Σn=1 n²+1 (-1)" sin 2nx) +Σn=1 n+1 (cos 2nx - n sin 2nx) (cos 2nx -n sin 2nx) 2nx)].

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Q: By computing the Fourier series of f(x) = x², show that n=1 1 n4 == 90°

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