Let $r_1,...,r_n$ and $\phi_1,...\phi_n$ be real numbers. Consider the following sum:
$S=\sum\limits_{k=1}^{n}r_k\sin(\phi_k+k\alpha)$
Suppose $S$ is constant for all $\alpha \in R$. Does it necessarily follow that $r_1=r_2=...=r_n=0$?
2026-03-28 19:35:59.1774726559
Can a sum of trigonometric functions equal a constant for all inputs?
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