Question

Brain teaser for the day:
Simplify \[\Large \prod_{k=0}^{n} \cos{(2^k \theta)}\]

Answer 1

people just love posting "cute" problems dont they :p

Answer 2

If you want a hint, multiply by 1.

Answer 3

hmm i dont know if that was a troll -___- haha

Answer 4

That was serious. =))

Answer 5

Generalized Morrie's law.

http://en.wikipedia.org/wiki/Morrie's_law

Answer 6

Aw man. Never knew that existed. Anyway, the "1" I was referring to was sin(x)/sin(x) and then repeatedly use sine double angle formula.