JEE-Advanced 2015 (20.A/40)

Geometry Level 4

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 \(2(a^2-b^2)=c^2\) and \(\lambda=\dfrac{\sin(X-Y)}{\sin Z}\), then find the possible value(s) of \(n\) for which \(\cos(n\pi\lambda)=0\). \[\begin{array}{} (1) \, 5 \quad \quad \quad \quad \quad \quad \quad \quad & (2) \, 3 \\ (3) \, 2 & (4) \, 1 \end{array}\] 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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