Well, the problem is:
For some reason I always get confused in verifying the identity ><;. Now, I tried various forms of doing it like changing sin4t to sin(2t+2t) but it just ends up getting jumbled up. Any help on how to not get so confused with "Verify the identity" problems or just pushing me in the right direction to solve this one would be appreciated.
In my substitution I let u=2t and because 4t = 2*2t it would be 2u. This can be expanded out to 2sin(u)cos(u).
However, because u=2t it must be put back in on that line so we get 2sin(2t)cos(2t). The u was to make the first step appear easier, you don't need to use it. The key to the question is knowing that sin(4t) = sin(2(2t)) so you can use the double angle formula with 2t +2t to simplify the 4t.
The next step is because the equation still needs to be simplified into terms of t so the double angle formulae can be used again