linear algebra - linearly independence of functions over $mathbb{R}$

I have been asked to prove that $\{\tan(ax)|a\in \mathbb{R}^+\}$ is linearly independent. I was wondering if there is a generic method/idea for proving linear independence of functions over $\mathbb{R}$.

Answer

Hint: Since $\tan \in C^{\infty}(\mathbf{R})$. Pick any finite number of $a_i$'s from $\mathbf{R}$. Show the Wronskian of $\tan{a_1x},\dots,\tan{a_nx}$ is nonzero.