If 12cot²θ - 31cosecθ + 32 = 0, 0° < θ < 90° then the value of tanθ will be:

12cot²θ - 31cosecθ + 32 = 0
12cosec²θ - 12 - 31cosecθ + 32 = 0
12cosec²θ - 31cosecθ + 20 = 0
12cosec²θ - 16cosecθ - 15cosecθ + 20 = 0
4cosecθ(3cosecθ - 4) - 5(3cosecθ - 4) = 0
(4cosecθ - 5)(3cosecθ - 4) = 0
cosecθ = $$\frac{5}{4}$$, cosecθ = $$\frac{4}{3}$$

$$ = \frac{{\sqrt 7 \times 3}}{7}$$

Alternate:
Go through option A

12cot²θ - 31cosecθ + 32 = 0
$$\eqalign{ & 12 \times \frac{9}{{16}} - \frac{{31 \times 5}}{4} + 32 = 0 \cr & 0 = 0 \cr} $$