Answer:
Option C
Explanation:
$12 \cot^{2}\theta - 31Cosec \theta + 32 = 0$
$\Rightarrow 12\left(cosec^{2}\theta-1\right)- 31Cosec \theta+32=0$
$\Rightarrow 12 cosec^{2}\theta- 31Cosec \theta+20=0$
$\Rightarrow 12 cosec^{2}\theta- 16Cosec \theta - 15 cosec\theta+20=0$
$(4 cosec\theta - 5)(3 cosec\theta-4)= 0$
$Cosec\theta = 5/4,4/3 \therefore \sin\theta = 4/5,3/4$
