If 0 ≤ α ≤ π/2 and 2sinα + 15 cos^2 α = 7 then the value of cot α is :

2 sin α + 15 cos$$^2$$ α = 7
Using: cos2 α = 1 - sin$$^2$$ α
2 sin α + 15 (1 - sin$$^2$$ α) = 7
2 sin α + 15 - 15 sin$$^2$$α = 7
15 sin$$^2$$ α - 2 sin α - 8 = 0
15 sin$$^2$$ α - 12 sin α + 10 sin α - 8 = 0
3 sin α (5 sin α - 4) + 2(5 sin α - 4) = 0
(5 sin α - 4)(3 sin α + 2) = 0
5 sin α - 4 = 0 or 3 sin α + 2 = 0
sin α = 4/5 or sin α = - 2/3
∵ 0 ≤ α ≤ π/2
∴ sin α = 4/5
cosec α = 5/4
cosec$$^2$$α = 25/16
1 + cot$$^2$$α = cosec$$^2$$α
1 + cot$$^2$$α = 25/16
cot$$^2$$α = (25/16) - 1 = 9/16
cot α = 3/4[∵ 0 ≤ α ≤ π/2]
Option C is the correct answer.