I have to prove the linear independence of $\{\sin^k(x)\}$, $ k\in \mathbb{N\_0}$.

I haven't ideas for proving it. Linearly independent means that we cannot find solution of this :
$\sin^{k\_1}(x) = \sum\_{i\ne k\_1} l\_i \cdot \sin^{i}(x)$ where $l\_i \in \mathbb{R}$.