Confusion regarding sinusoidal synthesis formula,
Simple:

Euler's formula:

$$ e^{i\theta} = \cos(\theta) + i \sin(\theta) $$

and

$$ e^{-i\theta} = \cos(\theta) - i \sin(\theta) $$

Add them together:

$$ e^{i\theta} + e^{-i\theta} = 2 \cos(\theta) $$

You should see that in your equation.

From there it is usually stated:

$$ \cos(\theta) = \frac{ e^{i\theta} + e^{-i\theta}}{ 2 } $$

See my article


The Exponential Nature of the Complex Unit Circle


for a more expansive explanation.