Matematické Fórum

stuart clark · 28. 07. 2014 08:57

If $2^{\sin x}+2^{\cos x}> 1$ . Then The Interval in which $x$ lies

Bati · 28. 07. 2014 09:49

It's easy to see that estimates
$2^{\sin{x}}\geq\tfrac12$ , $2^{\cos{x}}\geq\tfrac12$
and $2^{\sin{x}}+2^{\cos{x}}\geq1$ (*)
hold for an arbitrary $x$ . The equality in (*) would be attained only if $\sin{x}=-1$ and $\cos{x}=-1$ , but that's clearly not possible. Therefore, the sharp inequality (*) is valid for all $x$ .

stuart clark · 29. 07. 2014 19:17

Thanks ↑ Bati:

Matematické Fórum

#1 28. 07. 2014 08:57

Exp. Trig. Inequality

#2 28. 07. 2014 09:49

Re: Exp. Trig. Inequality

#3 29. 07. 2014 19:17

Re: Exp. Trig. Inequality

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