I have the equation $x^2 + x \cos(x) = 1 + \sin(x)$
and I need to prove that it has exactly two solutions.
What I used to do before when I had to prove an equation has one solution was:
used the intermediate value theorem to show there exists a solution and then used contradiction with Rolle's theorem to show that there's a unique one. But here I'm not so sure what to do.
Thanks for the help!