Question

iF x plus 1/x=2cosa,then x^n+1/x^n=?

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

$x+\frac{1}{x}=2cosa\\x^{2}-2xcosa+1=0\\WKT\\for \:ax^2+bx+c=0\\x=\frac{-b+\sqrt{b^2- 4ac}}{2a}\\x=\frac{-b-\sqrt{b^2- 4ac}}{2a}\\here\\x=\frac{2cosa+\sqrt{4cos^2a-4}}{2}\\x=\frac{2cosa+2isina}{2}\\x=cosa+sina=cisa\\Similarly\\x=\frac{2cosa-2isina}{2}\\x=cosa-sina=cis(-a)\\Now\\x^n+\frac{1}{x^n}\\(cosa+sina)^n+\frac{1}{(cosa+sina)^n}\\(cosa+sina)^n+(cosa-sina)^n\\Applying\; Demoivre"s\; Theorem\;for\; Integral \;Index\\ (cosna+sinna)+(cosna-sinna)\\2cosna\\since\\sin^2a+cos^2a=1$$i^{2}=-1$

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