Show the following propositions using a direct proof. (a) Proposition. If x is an even integer, then x² - 6x + 5 is odd. (b) Proposition. Suppose a, b, c ∈ Z. If a | b and a | c, then a | (b + c). (c) Proposition. g(x) = x³ - x⁴ - 5x² + 1 is an even function. (d) Using basic trigonometric identities, show 1 - cos²(x) = tan(x)cos(x)sin(x).