(Sin2t)(cos2t)

Alternatively you could go the other way!

sin(4t) = 2sin(2t)cos(2t)  so  sin(2t)cos(2t) = sin(4t)/2

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Once you work it out for yourself, you can check your answer at wolfram alpha

http://m.wolframalpha.com/input/?i=simplify+cos%282t%29+sin%282t%29&x=0&y=0&js=off

wolfram alpha often gives the answer in a number of alternative forms, so choose whichever one looks best to you!

$$\\(Sin2t)(cos2t)\\
=2sintcost(cos^2t-sin^2t)\\
=2sintcost(1-2sin^2t)\\$$

This is not going anyway - what form do you want it in?

That is a much better idea - Thanks Alan :)

I wish Icould give you double points for that.