Let t be a fixed number and let $\displaystyle c=cos(t)$ and $\displaystyle s=sin(t)$ and $\displaystyle \mathbf{x}=(c, cs, cs^2,..., cs^{n-1}, s^n)^T$.

Show that $\displaystyle \mathbf{x}$ is a unit vector.

Hint: $\displaystyle 1+s^2+s^4+...+s^{2n-2}=\frac{1-s^{2n}}{1-s^2}$

Not sure how that even helps unless I want to the hint via induction.