If x2−2xcosθ+1=0 , then the value of x2n−2xncosnθ+1  is:

The given equation is x2−2xcosθ+1=0 ⇒ x=2cosθ±4cos2θ−42         (∵ −b±b2−4ac2a )   x=2cosθ±2isinθ2=cosθ±isinθ∴ xn=cosnθ±isinnθand x2n=cos2nθ±isin2n θ∴ the required value is x2n−2xncosn θ+1=(cos2n θ±isin2nθ)−2(cosnθ±isinnθ)cosnθ+1 =(cos2n θ±isin2nθ)-(2cos2nθ±isin2nθ)+1=0