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

Answer: Option A

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
$$\begin{array}{rl}& 12\times \frac{9}{16}-\frac{31\times 5}{4}+32=0\\ & 0=0\end{array}$$