Trinometry

Geometry Level 3

If the value of $\displaystyle \prod_{i=1}^{10} \sin\left( \dfrac{i\pi}{11} \right)$ equals $\dfrac AB$ , where $A$ and $B$ are coprime positive integers, find $A+B$ .

The answer is 1035.

1 solution

Mateus Gomes
Feb 9, 2016

$\prod_{k=1}^{n-1}\sin(\frac{k\pi}{n})=\frac{n}{{2}^{n-1}}$ ${\boxed{n=11}}$ $\prod_{k=1}^{10}\sin(\frac{k\pi}{11})=\frac{11}{{2}^{10}}=\frac{11}{1024}=\frac{A}{B}$ $\Large\color{#3D99F6}{\boxed{A+B=1035}}$

https://www.youtube.com/watch?v=hQ532SjbxNo Here is a demostration of the identity

Juan Cruz Roldán - 7 months, 2 weeks ago

Trinometry

The answer is 1035.

1 solution

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