Mathematics

Problem

Let

-\frac{\pi}{6} < \theta < -\frac{\pi}{12}

. Suppose

\alpha_1

and

\beta_1

are the roots of the equation

x^2 - 2x \sec \theta + 1 = 0

, and

\alpha_2

and

\beta_2

are the roots of the equation

x^2 + 2x \tan \theta - 1 = 0

. If

\alpha_1 > \beta_1

and

\alpha_2 > \beta_2

, then

\alpha_1 + \beta_2

equals to a. 2(\sec \theta - \tan \theta) b. 2 \sec \theta c. -2 \tan \theta d. 0