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Prove that $$\sin(x) +\sin(3x)+\cdots + \sin((2n-1)x) = \frac{\sin^2(nx)}{\sin(n)}$$ where $n=1,2,3,\cdots$

This was done by my prof in lecture, but he went pretty quickly and I didn't really grasp what he was saying. Can anyone explain the proof for this problem?

Hlepkit
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1 Answers1

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take two g.p series , one of $cis x$ with ratio $cis^2 x$ and second $cis(\pi-x)$ with ratio $cis^2(\pi-x)$ and add them

avz2611
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