Why do I insert 2015 anywhere I like? #2

Geometry Level 5

log2[cos(2π2015)cos(4π2015)cos(6π2015)cos(4028π2015)]= ?\large{\log_2 \left[\cos \left( \dfrac{2 \pi}{2015} \right) \cos \left( \dfrac{4 \pi}{2015} \right) \cos \left( \dfrac{6 \pi}{2015} \right) \dotsm \cos \left( \dfrac{4028 \pi}{2015} \right) \right]} = \ ?


Bonus : Generalize k=02ncos(2kπ2n+1)\displaystyle \prod_{k=0}^{2n} \cos \left( \dfrac{2 k\pi}{2n+1} \right) in terms of nn with a proper derivation without using methods like Induction.

Try it's sister problem: Why do I insert 2015 anywhere I like? #1
×

Problem Loading...

Note Loading...

Set Loading...