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JEE Advanced 2016

JEE Main 2016 Mathematics question on Complex Numbers and Quadratic Equations

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 x2−2sec⁡θ+1=0x^2 - 2\sec\theta + 1 = 0, and α2\alpha_2 and β2\beta_2 are the roots of the equation x2+2tan⁡θ−1=0x^2 + 2\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
  1. A.
    2(sec⁡θ−tan⁡θ)2(\sec\theta - \tan\theta)
  2. B.
    2sec⁡θ2\sec\theta
  3. C.
    −2tan⁡θ-2\tan\theta
  4. D.
    00
Show answer

Correct option: C

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