If $2\,\,{\sin ^2}{\rm{\theta }} = 3\,\,\cos \,\,{\rm{\theta }},{\rm{\;}}0 \le {\rm{\theta }} \le 2{\rm{\pi }}$ then ${\rm{\theta }}$ is equal to

$\frac{{\rm{\pi }}}{3},\,\,\frac{{5\,{\rm{\pi }}}}{3}$

$\frac{{\rm{\pi }}}{6},\,\,\frac{{5\,{\rm{\pi }}}}{6}$

$\frac{{\rm{\pi }}}{3},\,\,\frac{{2\,{\rm{\pi }}}}{3}$

$\frac{{\rm{\pi }}}{2},{\rm{\;\pi }}$

JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

1 Medium

1 of 1

Application +4 | -1

2\,\,{\sin ^2}\mathrm{\theta } = 3\,\,\cos \,\,\mathrm{\theta },\mathrm{\;}0 \le \mathrm{\theta } \le 2\mathrm{\pi }

then

\mathrm{\theta }

is equal to

View answer and explanation

Correct option: C

\frac{\mathrm{\pi }}{3},\,\,\frac{{5\,\mathrm{\pi }}}{3}

Option C (

\frac{\mathrm{\pi }}{3},\,\,\frac{{5\,\mathrm{\pi }}}{3}

) is correct because these values of

\theta

satisfy the given trigonometric equation within the specified range of

0 \le \mathrm{\theta } \le 2\mathrm{\pi }