Question

If $12{\cot }^2\theta -31\text{coses}\theta +32=0$, then the value of $\sin \theta$ is

• A. $\frac{3}{5}$ or 1
• B. $\frac{2}{3}$ or $\frac{-2}{3}$
• C. $\frac{4}{5}$ or $\frac{3}{4}$
• D. $\pm \frac{1}{2}$

Answer 1

Answer: (C)

$12{\cot }^2\theta -31\text{cosec}\theta +32=0$
$\Rightarrow 12\left({\text{cosec}}^2\theta -1\right)-31\text{cosec}\theta +32=0$
$\Rightarrow 12{\text{cosec}}^2\theta -31\text{cosec}\theta +20=0$
$\Rightarrow 12{\text{cosec}}^2\theta -16\text{cosec}\theta -15\text{cosec}\theta +20=0$
$\Rightarrow (4\text{cosec}\theta -5)(3\text{cosec}\theta -4)=0$
$\Rightarrow \text{cosec}\theta =\frac{5}{4},\frac{4}{3};$
$\therefore \sin \theta =\frac{4}{5},\frac{3}{4}$