Question 50
For the real numbers $x$ and $\alpha$ we have
$$
x + \frac{1}{x} = 2 \cos \alpha .
$$
Prove that for all positive integers $n$
$$
x^n + \frac{1}{x^n} = 2 \cos(n \alpha) .
$$
$$
x + \frac{1}{x} = 2 \cos \alpha .
$$
Prove that for all positive integers $n$
$$
x^n + \frac{1}{x^n} = 2 \cos(n \alpha) .
$$