To determine the period of the given signal x[n], we need to analyze the individual terms and identify the least common multiple (LCM) of their periods.

(a) cos(5πn/9): The period of this term is given by T1 = 2π/ω = 2π/(5π/9) = 18/5.

(b) sin(4πn/7): The period of this term is given by T2 = 2π/ω = 2π/(4π/7) = 14/4 = 7/2.

To find the overall period of the signal, we need to find the LCM of T1 and T2.

LCM(18/5, 7/2) = (2 * 3 * 3 * 7) / (2 * 5 * 7) = 63

Therefore, the period of the signal x[n] = cos(5πn/9) + sin(4πn/7) is 63.