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I am trying to compute the Fourier series representation of a full wave rectifier output.

The equation of the signal is:

$ x_8(t) = | \cos (2 \pi f_o t) $ |

I have tried to find the Fourier series representation of the above signal but I ran with the following difficulties:

1) The solution given in the book is the following which is different from my answer:

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2) Surprisingly, my answer matches with the solution of the next problem given in the book which is:

Question: $ x_8(t) = | \cos (2 \pi f_o t) | + \cos (2 \pi f_o t) $ (Half Wave Rectifier Output)

Solution:

enter image description here

I am not able to understand whether what I have computed is correct or not. If it is incorrect what is the mistake that I have made? I am enclosing a copy of my answer sheet.

My Solution:

enter image description here

enter image description here

enter image description here

Thanks and regards.

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