The solution set of $(5 + 4\,\,\cos \,\,{\rm{\theta }})\,(2\,\,\cos \,\,{\rm{\theta }} + 1) = 0$ in the interval $\left[ {0,\;\,2{\rm{\pi }}} \right]$ is

$\left\{ {\frac{{2{\rm{\pi }}}}{3},\,\,\frac{{4{\rm{\pi }}}}{3}} \right\}$

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

$\left\{ {\frac{{\rm{\pi }}}{3},{\rm{\;\pi }}} \right\}$

$\left\{ {\frac{{2{\rm{\pi }}}}{3},\,\,\frac{{5{\rm{\pi }}}}{3}} \right\}$

JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

1 Easy

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Application +4 | -1

The solution set of

(5 + 4\,\,\cos \,\,\mathrm{\theta })\,(2\,\,\cos \,\,\mathrm{\theta } + 1) = 0

in the interval

\left[ {0,\;\,2\mathrm{\pi }} \right]

View answer and explanation

Correct option: C

\left\{ {\frac{{2\mathrm{\pi }}}{3},\,\,\frac{{4\mathrm{\pi }}}{3}} \right\}

Option C is correct because the solution set is found by solving the trigonometric equation and considering the interval [0, 2π].