If z+1z=2cosθ, then the value of z2n-1z2n+1

z+1z=2cosθ⇒z2-2cosθz+1=0⇒z=2cosθ±4cos2θ-42=cosθ±isinθ Taking positive sign, ∴  z2n-1z2n+1=2isinnθ2cosnθ=itannθ Taking negative sign, we get z2n-1z2n+1=-2isinnθ2cosnθ=-itannθ⇒z2n-1z2n+1=|±itannθ|=tannθ