1. Show the following propositions using a direct proof.
(a) Proposition. If a is an odd integer, then $a^3 + 3a + 5$ is odd.
(b) Proposition. Suppose $a, b \in \mathbb{Z}$. If $a|b$ then $a^2|b^2$.
(c) Proposition. $f(x) = \frac{x^2}{x - \frac{1}{x}}$ is an odd function.
(d) Use the identity $\sin^2(x) + \cos^2(x) = 1$, to show the identity $\tan^2(x) + 1 = \sec^2(x)$.