I have to use l'hopital's rule to show that for any fixed t, the limit as omega approaches 1, for $\displaystyle \frac{2}{1-\omega^2} (cos(\omega t) - cos(t) ) = tsin(t) $

To do this, I assume I must differentiate with respect to omega, so that means I am allowed to take t as a constant value?

Even if I am, I can't seem to be able to get there.. Any help would be greatly appreciated, cheers.