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

Dc term
Cosine terms
Sine terms
Odd harmonic terms

The correct answer is D. Odd harmonic terms.

A trigonometric Fourier series is a way of representing a periodic function as a sum of sine and cosine waves. The Fourier series of an even function only has cosine terms, because the sine terms are odd functions and therefore cancel out.

An even function is a function $f(x)$ such that $f(-x) = f(x)$. For example, the function $f(x) = x^2$ is even, because $f(-x) = (-x)^2 = x^2 = f(x)$.

An odd function is a function $f(x)$ such that $f(-x) = -f(x)$. For example, the function $f(x) = x$ is odd, because $f(-x) = -(-x) = x = f(x)$.

The sine function is an odd function, because $\sin(-x) = -\sin(x)$. The cosine function is an even function, because $\cos(-x) = \cos(x)$.

Therefore, the Fourier series of an even function only has cosine terms, because the sine terms are odd functions and therefore cancel out.

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