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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: find min value
Forum Index -> Trignometry like the article? email it to a friend.  
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[Post New]22 Apr 2008 18:40:27 IST
    Subject: find min value
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baba55 (17)

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find min value of 2sinx+ 2cosx
    
[Post New]22 Apr 2008 18:56:58 IST
    Subject: Re:find min value
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sboosy (2970)

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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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