Originally Posted by
DCB Thanks a lot for your help! It's much appreciated.
I think you may have made two small errors (either that or I misunderstood something)
I think (8y^{2}+6)√(1-y^{2})
should rightly be (8y^{2}-6)√(1-y^{2})
and you also dropped the 2 from 3y(1-2y^{3}) at the end. Unless I made some mistake.
In any case doing things the way you showed me I ended up with
16sin^{6}x-88sin^{4}x+105sin^{2}x-36
which I then factored and got 3 facts, 2 of which were the same, and one of which was impossible (sin(x)=±2 when simplified)
In any case the final answer, if I didn't mess up somewhere along the way, is x=pi/3, 2pi/3, or 4pi/3 in the given interval.
Thanks a lot for your help, I don't know if I ever would have found the answer without you.
Oh and sorry, for some reason I am heaving trouble with latex all of a sudden. I'll look into that later though.