# Fourier series representation of a full wave rectifier output

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:

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:

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:

Thanks and regards.