Homework Help: Aime 2008 Ii 8

[SOLVED] Aime 2008 Ii 8

1. The problem statement, all variables and given/known data
Let [itex]a = \pi/2008[/itex]. Find the smallest positive integer n such that
[tex]2[\cos(a)\sin(a)+\cos(4a)\sin(2a)+\cos(9a)\sin(3a)+\cdots+\cos(n^2a)\sin(na)] [/tex]
is an integer.

2. Relevant equations
[tex]\cos(a+b) = \cos a \cos b- \sin a \sin b[/tex]

[tex]\sin (a+b) = \sin a \cos b + \sin b \cos a[/tex]


3. The attempt at a solution
Can someone give me a hint please? This should only require high school math. I am not sure if the identities above are useful here or if there is a totally different method needed.

 

very nice