Trig Identities Help? Thanks!

Ok, I have a couple of questions on my homework that i just can't figure out how they work....

"Verify that each equation is an identity"

Cos^4(s)-sin^4(s) = cos2(s)

I'm a little confused as the how this could equal each other? I get the double angle identity (cos^2(x)-sin^2(x)=cos2x) But how would powers to the 4th simplify down?

And this one...

(sin4t/4) = cos^3(t)sin(t)-sin^3(t)cos(t)

I don't really even know where to begin on this one...We are working with double-angle identities and half-angle identities....

Thanks to anyone who can help!!