Find $\sum_{k=0}^6cot({\pi\over 21} + {k\pi\over 7})$

Question

Find $$\sum_{k=0}^6cot({\pi\over 21} + {k\pi\over 7})$$

I don't know how to do this at all. I initially started using complex numbers but couldn't get it.

Please give a simple solution.Thanks.

See http://math.stackexchange.com/questions/1607134/cotangent-summation-proof?lq=1 — lab bhattacharjee, Mar 17 '16 at 05:42

score 2 · Accepted Answer · answered Mar 17 '16 at 05:59

2

You can write it as $\frac{e^{ix}}{sin(x)}-i$ . Now we have $sin(x)=\frac{e^{ix}+e^{-ix}}{2i}$ now can you continue.

answered Mar 17 '16 at 05:59

Archis Welankar

1 Answers1