# JEE-Advanced 2015 (20.B/40)

**Geometry**Level 3

In a triangle \(\Delta XYZ\), let \(a,b\) and \(c\) be the lengths of the sides opposite to the angles \(X,Y\) and \(Z\) respectively. If \(1+\cos 2X-2 \cos 2Y=2 \sin X \sin Y\), then find the possible value(s) of \(\frac{a}{b}\). \[\begin{array}{} (1) \, 1 \quad \quad \quad \quad \quad \quad \quad \quad & (2) \, 2 \\ (3) \, 3 & (4) \, 5 \end{array}\] **Note :**

Submit your answer as the increasing order of the serial numbers of all the correct options.

For eg, if your answer is \((1),(2)\), then submit 12 as the correct answer, if your answer is \((2),(3),(4)\), then submit 234 as the correct answer.

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