According to the trigonometric identities, cos (x + y) = cos x cos y - sin x sin y. cos x = sin y and cos y = sin x via the complementary theorem. given the data, sin x = 5/13 and sin y = 4/6, then via substitution,
cos (x+y) = 4/6 * 5/13 - 5/13 * 4/6 = 0.
The answer hence is zero.
