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![[Post New]](/templates/default/images/icon_minipost_new.gif) 8 Dec 2007 11:55:13 IST
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If 2cos@ = x+1/x and 2cos# =y + 1/y,then:
prove that xmyn + 1/xmyn = 2cos(m@ + n#)
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8 Dec 2007 12:08:12 IST
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frm these data we get,
x^2 - 2cos@x + 1 = 0 and y^2 - 2cos#y + 1 = 0
on solving, x=cos@+/- isin@, y= cos# +/- isin#
taking the+ sign, x=ei@, y=ei#
just find x^my^n + 1/(x^my^n) = ei(m@+n#) + e-i(m@+n#)
= 2cos(m@+n#)
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8 Dec 2007 12:08:49 IST
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same can be proved using '-' sign also
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- Edward Everett Hale
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