Is it easy?

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SANZEED
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Is it easy?

Unread post by SANZEED » Tue Jun 05, 2012 12:36 am

Prove that if $x+\frac{1}{x}=2cos a$,then,
$x^{n}+\frac{1}{x^{n}}=2cos na$
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Phlembac Adib Hasan
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Re: Is it easy?

Unread post by Phlembac Adib Hasan » Tue Jun 05, 2012 8:59 am

SANZEED wrote: Is it easy?
Yes it is.By strong induction it's sufficient to prove \[cos(n+1)a=2cosna.cos a-cos (n-1)a\]\[=2cos (n-1)a.cos^2a-2sin(n-1)a.sina.cosa-cos(n-1)a\]\[=cos(n-1)a.cos2a-sin(n-1)a.sin2a\]\[=cos(n+1)a\]
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