Keaton Good

2022-01-27

$\mathrm{sin}\left(x\right)-x\mathrm{cos}\left(x\right)-\frac{1}{2}{x}^{2}=0$
I can verify that 0 is the solution of equation. But i don't have any method to show that is the only solution.

spelkw

HINT
Let indicate
$f\left(x\right)=\mathrm{sin}x-x\mathrm{cos}x-{\frac{12}{x}}^{2}⇒{f}^{\prime }\left(x\right)=x\mathrm{sin}x-x=x\left(\mathrm{sin}x-1\right)$

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