I need to prove: $$\sum_{r=0}^{n-1}\sin(\omega t-r\gamma)=\dfrac{\sin(\frac{1}{2}n\gamma)}{\sin(\frac{1}{2}\gamma)}\sin[\omega t-\dfrac{1}{2}(n-1)\gamma]$$
Hint: $\cos x-i\sin x=e^{-ix}$
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What does this have to do with "response of a array"? And why do you place that in the title? And what have you tried? – David G. Stork Apr 20 '20 at 19:28
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- Response of a seismic array....
– pymath Apr 20 '20 at 19:33 -
$$ \sum_{r=0}^{n-1}\sin(\omega t-r\gamma)=\text{Im}\left(\sum_{r=0}^{n-1}e^{i(\omega t-r\gamma)}\right) $$ – Tuvasbien Apr 20 '20 at 19:37
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Why does this question need to mention "seismic array"? – David G. Stork Apr 20 '20 at 19:55