The general value of $\theta $ that satisfies both the equations $cot^3\theta + 3 \sqrt 3 $ = $0$ & $cosec^5\theta + 32$ = $0$ is $(n \in I)$
$2n\pi - \frac{\pi }{6}$
$n\pi - \frac{\pi }{6}$
$n\pi - {\left( { - 1} \right)^n}\frac{\pi }{6}$
$n\pi + \frac{\pi }{3}$
Solve $\tan 2 x=-\cot \left(x+\frac{\pi}{3}\right)$
The number of points in $(-\infty, \infty)$, for which $x^2-x \sin x-\cos x=0$, is
The number of all possible triplets $(a_1 , a_2 , a_3)$ such that $a_1+ a_2 \,cos \, 2x + a_3 \, sin^2 x = 0$ for all $x$ is
The number of solutions of the pair of equations $ 2 \sin ^2 \theta-\cos 2 \theta=0 $, $ 2 \cos ^2 \theta-3 \sin \theta=0$ in the interval $[0,2 \pi]$ is
Statement $-1:$ The number of common solutions of the trigonometric equations $2\,sin^2\,\theta - cos\,2\theta = 0$ and $2 \,cos^2\,\theta - 3\,sin\,\theta = 0$ in the interval $[0, 2\pi ]$ is two.
Statement $-2:$ The number of solutions of the equation, $2\,cos^2\,\theta - 3\,sin\,\theta = 0$ in the interval $[0, \pi ]$ is two.