The trigonometric Fourier series of an even function of time does not have

The correct answer is: D. Odd harmonic terms

A trigonometric Fourier series of an even function of time is a series of sine and cosine terms of the form:

$$f(x) = a_0 + \sum_{n=1}^{\infty} a_n \cos(n \omega x) + b_n \sin(n \omega x)$$

where $a_0$ is the constant term, $a_n$ and $b_n$ are the coefficients of the cosine and sine terms, respectively,

and $\omega$ is the angular frequency.

The constant term, $a_0$, is present in the Fourier series of any function, even or odd.

The cosine terms, $a_n \cos(n \omega x)$, are present in the Fourier series of an even function if $n$ is even, and the sine terms, $b_n \sin(n \omega x)$, are present in the Fourier series of an even function if $n$ is odd.

Therefore, the Fourier series of an even function of time does not have odd harmonic terms.