If $$\alpha$$ is a positive acute angle and $$2sin\alpha + 15cos^{2}\alpha = 7$$, then the value of cota is:2

sin²$$\alpha$$ +cos²$$\alpha$$ =1 (identity)
cos²$$\alpha$$ = 1-sin²$$\alpha$$
2sin$$\alpha$$ +15cos²$$\alpha$$ =7
put 1-sin²$$\alpha$$ instead of cos²$$\alpha$$
2sin$$\alpha$$ +15(1-sin²$$\alpha$$) =7
-15sin²$$\alpha$$ +2sin$$\alpha$$ +8=0
Let sin$$\alpha$$ = x
-15x² +2x +8=0
Solving for x we get,
x= 4/5 and x = -2/3
x = 4/5 is the real solution
sin $$\alpha$$= 4/5
sin² $$\alpha$$= 16/25
sin²$$\alpha$$+cos²$$\alpha$$=1 = sin²$$\alpha$$ = 1-cos²$$\alpha$$
1-cos²$$\alpha$$ =16/25 = cos²$$\alpha$$ =9/25 = cos$$\alpha$$ =3/5
cot $$\alpha$$ = cos $$\alpha$$ / sin $$\alpha$$ = (3/5) / (4/5) = 3/4
Option A is the correct answer.