Linear combinations of trigonometric functions?

So I'm reading a book on physical chemistry to prepare for the GRE subject tests. One of the end-of-chapter problems asks me to show that x(t) = Acos(ωt) + Bsin(ωt) oscillates with the same frequency as x(t) = cost(ωt), which is equal to ω/2π. The solution states that because each term in the sum has that frequency, then a linear combination of them will also have that frequency. This makes intuitive sense, but I was curious as to how it could be shown mathematically.