1. The problem statement, all variables and given/known data Let A(x) = a0 + a1x + a2x2 + a3x3 + ... = Ʃanxn. Express E(x) = a0 + a2x2 + a4x4 + ... = Ʃa2nx2n. Do the same for O(x) = a1x + a3x3 + a5x5 + ... 2. Relevant equations A(x) = a0 + a1x + a2x2 + a3x3 + ... = Ʃanxn 3. The attempt at a solution So I tried using A(x2) as a starting point, but got stuck on how to get the coefficients of A(x2) = a0 + a1x2 + a2x4 + a3x6 + ... to match those of E(x). How would I begin expressing E(x) and O(x) in terms of A(x)? Could there be something I could do with sin or cos?