If the equation ${\sin ^2}\,\,{\rm{\theta }} - \cos \,\,{\rm{\theta }} = \frac{1}{4}$, then the value of ${\rm{\theta }}$ lying in the interval $0\,\, \le \,\,{\rm{\theta }}\,\, \le \,\,2{\rm{\pi }}$ is

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

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

$\frac{{4\,{\rm{\pi }}}}{3},\,\,\frac{{5\,{\rm{\pi }}}}{3}$

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

JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

1 Easy

1 of 1

Application +4 | -1

If the equation

{\sin ^2}\,\,\mathrm{\theta } - \cos \,\,\mathrm{\theta } = \frac{1}{4}

, then the value of

\mathrm{\theta }

lying in the interval

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

View answer and explanation

Correct option: A

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

Option A (

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

) is correct because these values of

\theta

satisfy the given equation

{\sin ^2}\,\mathrm{\theta } - \cos \,\mathrm{\theta } = \frac{1}{4}

within the interval

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