Let `-1/6 < theta < -pi/12` Suppose `alpha_1 and beta_1`, are the roots of the equation `x^2-2xsectheta + 1=0` and `alpha_2 and beta_2` are the

Question

Let `-1/6 < theta < -pi/12` Suppose `alpha_1 and beta_1`, are the roots of the equation `x^2-2xsectheta + 1=0` and `alpha_2 and beta_2` are the roots of the equation `x^2 + 2xtantheta-1=0`. If `alpha_1 > beta_1` and `alpha_2 >beta_2`, then `alpha_1 + beta_2` equals
A. `2(sec theta - tan theta)`
B. `2 sec theta `
C. ` - 2 tan theta `
D. 0

Answer 1

Correct Answer - 4
Solving given equations and from given values of ` theta` which lie
in fourth quadrant
` alpha_(1) = sec theta - tan theta `
` beta_(1) = sec theta + tan theta`
` alpha _(2) sec theta - tan theta `
` beta _(2) = - sec theta - tan theta `
` alpha_(1) + beta_(2) = - 2 tan theta ` .