Solution of $\tan(nx)=k\tan(x)$ Could you kindly suggest me ways to find out closed form solution of the following equation type:
$$\tan(nx)=k\tan(x),$$
where $n$ and $k$ are some positive real numbers (that excludes zero). I can solve it using series expansion, but that gives me only an approximate solution for $x$.
Thanks in advance.
PS: I am in engineering stream, but I usually don't need to solve problems that seems very tough to me, mostly just couple of additions/subtractions etc.

I think i have a trivial solution . If $n=k=1$ and $x=45$ then we have $\tan(1\cdot45)=1\tan(45)$ so $1=1$.
