Trigonometric Identity Evaluation (Jee Mains)

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Trigonometric Identity Evaluation

If $\frac{{{{\cos }^2}48^\circ - {{\sin }^2}12^\circ}}{{{{\sin }^2}24^\circ - {{\sin }^2}6^\circ}} = \frac{{\alpha + \beta \sqrt 5 }}{2}$ , where α, β ∈ ${\Bbb N}$ , then α + β is equal to _______.

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