Can I consider that cos(a)+cos(b) != cos(a+b)

because it not a linear function?

In the definition of linear function a & b are vectors.

I know from physics that vector is contain size and angle.

So I can say because a & b are not vectors and the expression isn't linear function, this is the reason that the expression isn't valid?

and: When the expression is consider valid?

the expression:

cos(a)+cos(b)=cos(a + b).