x^2+1/x^2=(x+1/x)^2-2=(2cosθ)^2-2=4cos^2θ-2=2(2cos^2θ-1)=2cos2θx^3+1/x^3=(x+1/x)(x^2+1/x^2-1)=2cosθ(4cos^2θ-2-1)=2cosθ(4cos^2θ-3)=2(4cos^3θ-3cosθ)=2cos3θ.x^n+1/x^n=2cosnθ