Thread: Simplify trig equation using identities

So I need to simplify a problem down to ten characters, and I got this far and now I'm stuck:

2cos3t(3sint-4sin³t) +1

I don't really know what to do with the 2cos3t... I feel like distributing it in would just make the problem even messier...

Here's the original problem:
2cos(3t)(sin(2t)cos(t)+cos2t* sqr(1-cos²t))+1

Here's what I was able to do:
I turned the (sin2tcost)
into 2sintcost(cost)
then into 2sintcos²t,
then into 2sint(1-sin²t),
then into 2sint-2sin³t.

Then I turned cos2t*sqr(1-cos²t)
into 1-2sin²t*sqrt(sin²t),
then into 1-2sin²t(sint),
then into sint-2sin³t.

Then I added the two sides together to get 3sint-4sin³t

Right now we're using reciprocal id, quotient id, pythagorean id, cofunction id, even/odd id, sum&difference formulas, half-angle formulas, double angle formulas, sum-to-product formulas


Any help would be fantastic! Thanks!