# Ratio of two tanned alternate signed even-odd binomial summation

Geometry Level 5

$\large R=\dfrac{\displaystyle\sum_{r=1}^{2k} (-1)^{r-1}\binom{4k}{2r-1}\tan^{2r-1}\theta}{\displaystyle\sum_{r=0}^{2k} (-1)^{r}\binom{4k}{2r}\tan^{2r}\theta}$

Find the value of $$R$$ if $$k=100$$ , $$\theta = \dfrac{\pi}{480}$$.