Hi,
That doesnt seem to be the case if all we are doing is computing the Fourier Transform.
When i compute the Fourier Transform directly of cos(wt) i get (d here is the curly delta symbol for an impulse):
pi*[d(w-wo)+d(w+wo)]
but when i compute the Fourier Transform of -cos(wt) directly i get:
-pi*[d(w-wo)+d(w+wo)]
which is the negative of the first solution.
This looks correct because any constant carries through an integration, and in the next to last step in the limit i get either 1/2 or -1/2 where clearly one is the negative of the other. Multiplied by 2*pi we get either pi or -pi as shown above.
Also, simpler is two applications of (d as above):
e^(j*wo*t) <=> 2*pi*d*(w-wo)
As noted, 'd' above is used in place of the symbol 'δ'.