How do you reduce this trig equation to solve for x?

Question

$$x \cos(x) = \sin(x)$$

For the life of me I am unable to think of a way to solve for $x$. Wolfram Mathematica couldn't even find a way to solve it!

Answer 1

Note that

$$x\cdot \cos x=\sin x \iff \tan x = x$$

which has the trivial $x=0$ and infinitely many other solutions.

Answer 2

It's easy to divide by $\cos$ on both sides and find that you want solutions to $x=\tan x$, but I doubt that has many solutions expressible by elementary functions (the trivial solution $x=0$ obviously is).