(sin x/x)^2+tg x/x>2

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Cezar Lupu
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(sin x/x)^2+tg x/x>2

Post by Cezar Lupu »

Sa se arate ca

\( \left(\frac{\sin x}{x}\right)^{2p}+\left(\frac{\
tan x}{x}\right)^{p} >2 \)

pentru orice \( p\geq 0 \) si \( x\in\left(0, \frac{\pi}{2}\right) \).


Murray Klamkin, Crux Mathematicorum


Observatie. Inegalitatea de mai sus intareste si conditia impusa in articolul de aici.
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.
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