Can anybody explain me this fourier series page in simple steps

**Fourier Series for Even Functions **

For an **even** function *f*(*t*), defined over the range -*L* to *L* (i.e. period = 2*L*), we have the following handy short cut.

Since

and

*f*(*t*) is even,

it means the integral will have value 0. (See Properties of Sine and Cosine Graphs.)

So for the Fourier Series for an even function, the coefficient *b**n *has zero value:

*b**n*** = 0**

So we only need to calculate *a*0 and *an* when finding the Fourier Series expansion for an even function *f*(*t*):

**http://www.intmath.com/Fourier-series/Image91.gif** http://www.intmath.com/Fourier-series/Image92.gif

An **even** function has only **cosine** terms in its Fourier expansion:

**Specally how he has written ao/2 in last equation. Thanks**