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)

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