Addition of Two Cosine Functions Into a Single Cosine Function

Question

Recently I was looking at modelling tides with the form of $a*\cos(bx)+c*\cos(dx)$. Can I combine these two terms into a single function? I realise that $\cos(bx)+\cos(dx)$ becomes $2\cos\bigl(\frac{(b+d)}{2}\bigr)*\cos\bigl(\frac{(b-d)}{2}\bigr)$, and that I can take $a$ out as a common factor; how do I combine $a*\cos(bx)+c*\cos(dx)$ into one cosine function?