How to solve it without integrals: \sum_{k=1}^n \sin (\frac{k \pi}{n})

Stefan Hendricks

Stefan Hendricks

Answered question

2022-01-17

How to solve it without integrals:
k=1nsin(kπn)sin(kπn2)

Answer & Explanation

MoxboasteBots5h

MoxboasteBots5h

Beginner2022-01-18Added 35 answers

HINTS: Use the identity
sin(x)sin(y)=12cos(xy)12cos(x+y)
and then use the fact the
k=1ncos(ak)=csc(a2)sin(an2)cos(a(n+1)2)
where a does not depend on k, but can certainly depend on n.

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