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 $$\sum_{k=0}^{44}\tan(4k+1)^\circ = 45$$
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Your title does not match the question's body. – Torsten Schoeneberg Dec 09 '17 at 17:01
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My bad, I will fix it :) – Ziad Fakhoury Dec 09 '17 at 17:04
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2A reference to this can be found here – lulu Dec 09 '17 at 17:10
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@lulu, thank you very much that is exactly what I was looking for :) – Ziad Fakhoury Dec 09 '17 at 17:26
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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
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@labbhattacharjee, we should have a simple solution for this problem. – xpaul Dec 12 '17 at 14:52
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@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