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## Homework Statement

Let n be a natural number.

Prove that the equation: [tex]x^{2}(cos(x))^{n}+xsin(x)+1=0[/tex] has an infinite amount of solutions.

## The Attempt at a Solution

I named that equation f(x)=0 and I said that f(a)<f(0)<f(b) and that f(a) x f(b) < 0.

Should I choose n=1 and chose a=0 and b=pi ? I know that the equation is a period equation so it will have an infinite amount of solutions, but i'm not sure how to show it because I've only been dealing with equations that want you to show there is at least one solution in [a,b]. Any help would be really appreciated. Thank you.