From:
$g(t)\sin\left(\omega_{0}t\right)\Leftrightarrow \frac{1}{2j}[G(\omega-\omega_{0})-G(\omega+\omega_{0})]$
Prove that:
$G(\omega)\sin\left(\omega T\right)\Leftrightarrow \frac{1}{2j}[g(t+T)-g(t-T)]$
USING the time-frequency duality property:
$G(t)\Leftrightarrow 2 \pi g(-\omega)$
I'm stuck and I can't get rid of the 2pi multiplying nor the g(-w)
Thanks in advanced