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JEE Advanced 2016 Paper 1 Mathematics Question 37


Let \(-\frac{\pi}{6} < \theta < -\frac{\pi}{12}\). Suppose \(\alpha_1\) and \(\beta_1\) are the roots of the equation \(x^2 - 2 x \text{sec}\theta + 1 = 0\) and \(\alpha_2\) and \(\beta_2\) are the roots of the equation \(x^2 + 2x \text{tan} \theta - 1 = 0\). If \(\alpha_1 > \beta_1\) and \(\alpha_2 > \beta_2\), then \(\alpha_1 + \beta_2\) equals