Could anyone help me on this,(adsbygoogle = window.adsbygoogle || []).push({});

Is it true that for any given [itex]r_{1},r_{2},r_{3},r_{4}>0[/itex] and [itex]t_{1},t_{2},t_{3},t_{4}\in[0,2\pi)[/itex] if

[itex]r_{1}\left|\cos(t-t_{1})\right|+r_{2}\left|\cos(t-t_{2})\right|[/itex][itex]<r_{3}\left|\cos(t-t_{3})\right|+r_{4}\left|\cos(t-t_{4})\right|[/itex] for all [itex]t\in[0,2\pi)[/itex]

then [itex]r_{1}+r_{2}<r_{3}+r_{4}[/itex] ?

By the way, this is not a homework problem.

Any help will be highly appreciated!

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# A basic inequality

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