Expression: $\cos\left({α+β}\right)\cos\left({β}\right)-\sin\left({α+β}\right)\sin\left({β}\right)$
Use $\cos\left({t}\right)\cos\left({s}\right)-\sin\left({t}\right)\sin\left({s}\right)=\cos\left({t+s}\right)$ to simplify the expression $\cos\left({α+β+β}\right)$
Collect like terms $\cos\left({α+2β}\right)$