Y by
Hello AoPS Community,
I am curious about how to demonstrate the following inequality:
I’ve plotted the functions, and the inequality seems to hold. However, I am looking for a rigorous way to prove it.
I’d greatly appreciate insights into how to break this down analytically and references to similar problems or techniques that might be helpful.
Thank you so much for your guidance and support!
I am curious about how to demonstrate the following inequality:
\sqrt{1 - |\cos(x \pm y)|^a} \leq \sqrt{1 - |\cos(x)|^a} + \sqrt{1 - |\cos(y)|^a}, \quad \text{for } a \geq 1.
I’ve plotted the functions, and the inequality seems to hold. However, I am looking for a rigorous way to prove it.
I’d greatly appreciate insights into how to break this down analytically and references to similar problems or techniques that might be helpful.
Thank you so much for your guidance and support!