It Cos theta plus cos theta not that sighn

The problem statement from the image you sent is:
"Given that $\cos\theta + \cos\phi = P$ and $\sin\theta + \sin\phi = Q$, prove that $\cos(\theta - \phi) = \frac{1}{2}(P^2 + Q^2 - 2)$."

Notice that the problem explicitly gives one equation with cosines ($\cos\theta + \cos\phi = P$) and another equation with sines ($\sin\theta + \sin\phi = Q$). My solution uses both of these distinct equations exactly as provided.

Let's go through it one more time, focusing on how each given equation is used.

:
Given $\cos\theta + \cos\phi = P$ and $\sin\theta + \sin\phi = Q$, prove that $\cos(\theta - \phi) = \frac{1}{2}(P^2 + Q^2 - 2)$.