Derive abbreviation of cos(a+summation(b))

[baby_1]

Homework Statement

I want to derive these equations

Homework Equations

The Attempt at a Solution

But I don't have any idea how can extend cos(summation) and sin(summation) in form of Bessel function or product of Sin(wmt+phim)

 

[mfb]

The first step is using cos(x) = Re(e^ix)