a.) Prove that the even (odd) degree Legendre polynomials are even (odd) functions of $t$.
b.) Prove that if $p(t) = p(-t)$ is an even polynomial, then all the odd order coefficents $c_{2j+1} = 0$ in its Legendre expansion $p(t) = c_0q_0(t) + ... + c_nq_n(t)$ vanish.
Is "a" similar to proving that Legendre polynomials of even and odd degree are orthogonal and for "b" I do not know how to do.