start with the identity tan^{2}θ + 1 = sec^{2}θ
substituting, 2(sec^{2}θ  1) = 5 secθ + 10 giving an equation in secθ.
substituting x = secθ
2(x^{2}  1) = 5x + 10, 2x^{2} 5x 12 = 0
Using the quadratic formula, x = (5 ± √(25 + 96))/4, or x = 4, or x = 3/2
Since x = secθ, and since the angle is obtuse (between 90 and 180 degrees), secθ = 3/2 , so cosθ = 2/3 and sinθ = √(5/9) = √5/3, and tanθ = √5/2
2/8/2014

Kenneth G.