Show that if a periodic signal x(t) is an even function of t, then all the sine terms in its trigonometric Fourier series vanish, and if x(t) is an odd function of t, all the cosine terms vanish. In...

Show that if a periodic signal x(t) is an even function of t, then all the sine terms in its trigonometric Fourier series vanish, and if x(t) is an odd function of t, all the cosine terms vanish. In either case, show that to compute the Fourier coefficients, we need to evaluate integrals over only half the period.