Prove this equation using trigonometric identities

I need to prove this:

$U\cos (w_mt-\alpha _1)\cos(w_0t)-U\sin(w_mt-\alpha _2)\sin(w_0t)=U\left \{ \cos \frac{\alpha_2-\alpha_1}{2} \cos\left [ (w_0+w_m)t-\frac{\alpha_1+\alpha_2}{2} \right ]+ \sin \frac{\alpha_2-\alpha_1}{2}\sin\left [ (w_0-w_m)t+\frac{\alpha_1 +\alpha_2}{2} \right ]\right \}$

More precisely, I should start with left side of equation, use some trigonometric identities to get right side of equation. Any idea? I tried some identities but I with no success.