Cosine of an Integer

Geometry Level 3

\[ \tan\left(\dfrac{\pi}{12}\right) = \sqrt{\dfrac{a-\sqrt{b}}{a+\sqrt{b}}}\]

If the equation above holds true for integers \(a\) and \(b\) with \(b\) square-free, find \(a\times b\).

Hint: Use double angle identities.

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