JEE Advanced 2016 Paper 1 Mathematics Q1

Mathematics

Problem

Let −π6<θ<−π12-\frac{\pi}{6}<\theta<-\frac{\pi}{12}. Suppose α1\alpha_1 and β1\beta_1 are the roots of the equation x2−2xsec⁡θ+1=0x^2-2x\sec\theta+1=0 and α2\alpha_2 and β2\beta_2 are the roots of the equation x2+2xtan⁡θ−1=0x^2+2x\tan\theta-1=0. If α1>β1\alpha_1>\beta_1 and α2>β2\alpha_2>\beta_2, then α1+β2\alpha_1+\beta_2 equals

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