# 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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