If (cos²48° − sin²12°)/(sin²24° − sin²6°) = (α + β√5)/2
where α, β ∈ N, find α + β.

Solution:

Using trigonometric identities and simplification,

(cos²48° − sin²12°)/(sin²24° − sin²6°) = (3 + √5)/2

Comparing with:
(α + β√5)/2

α = 3 and β = 1

Therefore,
α + β = 3 + 1 = 4