x (t) is a real valued function of a real variable with

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x (t) is a real valued function of a real variable with period T. Its trigonometric Fourier Series expansion contains no terms of frequency
ω = 2π (2k)/T; k = 1, 2,.... Also, no sine terms are present. Then x (t) satisfies the equation

1. x (t) =– x (t – T)
2. x (t) = x (T – t) = – x (– t)
3. x (t) = x (T – t) = – x (t – T/2)
4. x (t) = x (t – T) = x (t – T/2)

Correct Option: D

Since, the fourier expansion of x(t) contains no sine terms, therefore,
x(t) = x(–t)
or, x(t) = x(T – t)
as x(t) is periodic with T
Now, as signal x(t) contains odd harmonics.

Then x(t) = -x		t -	T
			2

Thus x(t) = x(T - t) = -x		t -	T
			2