If $x+\frac{1}{x}=2 \cos \theta$, then for any integer $n, x^n+\frac{1}{x^n}=$

Question

If $x+\frac{1}{x}=2 \cos \theta$, then for any integer $n, x^n+\frac{1}{x^n}=$, $2 \cos n \theta$, $2 \sin n \theta$, $2 i \cos n \theta$, $2 i \sin n \theta$

MARKS App · Accepted Answer

Hints: $x+\frac{1}{x}=2 \cos \theta$ Let $x=\cos \theta+1 \sin \theta$ $\frac{1}{x}=\cos \theta-1 \sin \theta$ Thus $x^n+\frac{1}{x^n}=2 \cos n \theta$

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