# A geometry problem by Bala vidyadharan

Geometry Level 3

$\begin{cases} a= \cos\alpha +\cos\beta \\ b = \sin\alpha +\sin\beta \\ 2\theta = \alpha -\beta \\ \end{cases}$

If $$\alpha , \beta, a,b$$ and $$\theta$$ satisfy the system of equations above, state the value of $$\dfrac{\cos(3\theta)}{\cos(\theta)}$$ in terms of $$a$$ and $$b$$.

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