Puzzle | Pell numbers – inequality

 

To prove the inequality:
 

PELL NUMBERS 2

 

Hint :

 
For all real numbers   x   and   y   with   0 < y < \pi/2,

we have

\sin x + \cos x \; = \; \sqrt{2} \: \sin (x + \pi/4) \: \leq \: \sqrt{2} \: < \: 3/2 \: \leq \: 3/2 \: \sec y

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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