Solution
= Solution
Every finite sum of the <sine> modes is <odd>, and so is a limit in the <L2 norm> of such sums. In contrast, $x^2-1$ is a nonzero <even function>. Its <inner product> with every <odd> <sine> mode vanishes, so all its proposed <Fourier sine series> coefficients would be zero. \b[It cannot be represented by this basis on the symmetric interval.] An <even> <Fourier cosine series> is the appropriate alternative there.