Question

: Linear Algebra: Let t be a fixed real number and let c = cos t, s = sin t, vector x = (c, cs, cs^2, ..., cs^(n-1), s^n)^T. Show that the vector x is a unit vector in R^(n+1).

Answer 1

Book's hint: \[1 + s^2 + s^4 + ... + s^{2n-2} = (1-s^{2n})/(1-s^2)\]