Question

How to solve: Sin(x)=x^2-pi^2

Answer 1

Rewrite the equation as

$\sin(x) = x^2-\pi^2 = (x-\pi)(x+\pi)$

If we choose $x=\pm\pi$, the right hand side becomes zero, and so does the left hand side.

If you graph the two functions $f(x) = \sin(x)$ and $g(x) = x^2-\pi^2$, you'll see that there are only two solutions, so the ones we found are the only ones.