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If $x=\cos\theta+i\sin\theta $ the value of $x^{n}+\large\frac{1}{x^{n}}$ is

\[\begin{array}{1 1}(1)2\cos n\theta&(2)2\;i\sin n\theta\\(3)2\sin n\theta&(4)2\; i\cos n\theta\end{array}\]

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$x= \cos \theta+ i \sin \theta$
$x^n= (\cos \theta+ i \sin \theta)^n$
$x^n= \cos n \theta+ i \sin n\theta $
$\large\frac{1}{x^n} $$= \cos n \theta+ i \sin n\theta $
$\qquad= 2\cos n\theta$
Hence 1 is the correct answer.
answered May 14, 2014 by meena.p
 

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