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[Post New]22 Apr 2008 18:56:58 IST
    Subject: Re:find min value
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sboosy (3063)

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Olaaa!! Perrrfect answer. 539  [723 rates]
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\frac{2^{\sin(x)}+2^{\cos(x)}}{2} \geq 2^{\frac{\sin(x)+\cos(x)}{2}} \ \mbox{(Using AM-GM)} \\ \\ \sin(x)+\cos(x) \geq -\sqrt{2} \ \Rightarrow \frac{\sin(x)+\cos(x)}{2} \geq -\frac{1}{\sqrt{2}} \\ \\ \frac{2^{\sin(x)}+2^{\cos(x)}}{2} \geq 2^{\frac{-1}{\sqrt{2}}} \\ \\ 2^{\sin(x)}+2^{\cos(x)} \geq 2^{1-\frac{1}{\sqrt{2}}}
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