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

$\frac{2}{3}$ or $ - \frac{2}{3}$

JEE MATHEMATICS MCQ: TRIGONOMETRY RATIOS

1 Easy

1 of 1

Application +4 | -1

12\,\,{\cot ^2}\,\,\theta - 31\;\,\,\mathrm{cosec}\;\,\,\theta + 32 = 0

, then the value of

\sin \,\,\theta

View answer and explanation

Correct option: C

\frac{}{5}

\frac{3}{4}

Option C (

\frac{4}{5}

\frac{3}{4}

) is correct because solving the trigonometric equation

12{\cot ^2}\theta - 31\mathrm{cosec}\theta + 32 = 0

leads to

\sin \theta = \frac{4}{5}

\sin \theta = \frac{3}{4}