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Expanding Trig Power Identities


How can I use Mathematica to find the expansion of various trigonometric power
identities?  I've already tried TrigExpand w/o succes.

I have functions of the form Sin[a](Sin[b])^n  and  Cos[a](Cos[b])^n 
where n is a power.

I would like to get the fully expanded version of these functions, so
that there are no more powers involved.  If n=1 then the answer is
just the standard product relations that you can look up in the back
of any trig book.  But I need to be able to do it for higher powers of
n.  And I don't know how to even do it for n=1.


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