If a and theta are real numbers such that x + 1/x = 2cos(theta), then:
x^n +1/x^n = 2cos(n*theta)
x + 1/x = 2cos(theta)
The Attempt at a Solution
So I was able to show that the statement was true for n=1, but I'm stuck on how to even start proving it for n+1. I tried x^(n+1) + 1/x^(n+1), thinking I could solve it for n+1, but to no avail. Help, please?