12. Let $0<\theta<\pi, x+\frac{1}{x}=2 \cos \theta$, then $x^{n}+\frac{1}{x^{n}}$ can be expressed in terms of $n$ and $\theta$ as
12. $2 \cos n \theta$ Let $x=\cos \theta \pm i \sin \theta$, so $x^{n}+\frac{1}{x^{n}}=2 \cos n \theta$.