I found the following text -

> 
> The functions $\cos (nx), n = 0, 1, 2, \cdots$ and $\sin (nx), n = 1, 2, \cdots $ which are known to be orthogonal with respect to the
> standard scalar product on $(-\pi, \pi)$.
> 
> 
> 

The source of the problem is -

[![enter image description here](https://i.stack.imgur.com/tW6hy.jpg)](https://i.stack.imgur.com/tW6hy.jpg)

**Question:** Plz explain why we author needed to mention
"..the functions $\cos (nx), n = 0, 1, 2, \cdots$ and $\sin (nx), n = 1, 2, \cdots $ which are known to be orthogonal with respect to the standard scalar product on $(-\pi, \pi)$".... as we dont need the scalar product of $\cos (nx), \sin (nx)$ in the above example?

**Note:**

We are doing scalar product of $f$ and $\sin nx$, scalar product of $f$ and $\cos nx$, scalar product of $\sin nx$ and $\sin nx$, scalar product of $\cos nx$ and $\cos nx$, but we never used scalar product of $\cos nx$ and $\sin nx$, then why it was mentioned? what is the meaning of that part of the sentence?
Thanks.