a cosθ + b sinθ = c where c2 ≤ a2 + b2 

Divide each term by √(a2 + b2)

cosθ cosα + sinθ sinα = cosβ

cos (θ − α) = cosβ

θ − α = 2nπ ± β

θ = 2nπ + α ± β, n ∈ Z