I have a homework question to prove that
$x \sin x+\cos x=x^2$
has only one positive solution.
I have easily proved that it has a positive answer by showing that $f(x)=x\operatorname{sin}x+\operatorname{cos}x-x^2$ is smaller then $0$ at $f(\frac{\pi}{2})$ and larger then $0$ at $f(0)$ and then using the Intermediate Value Theorem.
But I am having trouble proving this is the only positive solution. Can someone help me with this? Thanks :)