Evaluate: cos(α+β)cos(β)-sin(α+β)sin(β)

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

$\cos\left({α+2β}\right)$