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Last edited by 1+1=？ 2025-6-5 23:05\[
\begin{aligned}
& \forall y \geq 1, x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right): \\
& \frac{(y-1)\left(\frac{x y}{\sin (x)}\right)^{y-\cos (x y)}}{y^{y-\sin (x y)}}+\frac{\left(y \sqrt{1-\frac{4}{\pi^2} x^2}\right)^{\sin (x y)-y}}{y^{\cos (x y)-y}} \geq y^{1+\sqrt{2} \sin \left(x y-\frac{\pi}{4}\right)}
\end{aligned}
\]
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