I want a way to solve this series without resorting to the ugly expansion of $\tan nx$. Can anyone help? (the angles are in degrees)
Show that $$\sum_{k=0}^{44}\tan(4k+1)^\circ = 45$$
Asked
Active
Viewed 96 times
0
-
Your title does not match the question's body. – Torsten Schoeneberg Dec 09 '17 at 17:01
-
My bad, I will fix it :) – Ziad Fakhoury Dec 09 '17 at 17:04
-
2A reference to this can be found here – lulu Dec 09 '17 at 17:10
-
@lulu, thank you very much that is exactly what I was looking for :) – Ziad Fakhoury Dec 09 '17 at 17:26
-
Use https://math.stackexchange.com/questions/346368/sum-of-tangent-functions-where-arguments-are-in-specific-arithmetic-series – lab bhattacharjee Dec 09 '17 at 18:20
-
@labbhattacharjee, we should have a simple solution for this problem. – xpaul Dec 12 '17 at 14:52
-
@xpaul, Not sure if the answer linked here is too complex! Just put $$\theta=1^\circ, n=45$$ – lab bhattacharjee Dec 12 '17 at 14:55