The general value of $\theta $ that satisfies both the equations $cot^3\theta + 3 \sqrt 3 $ = $0$ & $cosec^5\theta + 32$ = $0$ is $(n \in I)$
$2n\pi - \frac{\pi }{6}$
$n\pi - \frac{\pi }{6}$
$n\pi - {\left( { - 1} \right)^n}\frac{\pi }{6}$
$n\pi + \frac{\pi }{3}$
The solution of the equation $4{\cos ^2}x + 6$${\sin ^2}x = 5$
If $\alpha ,\,\beta ,\,\gamma ,\,\delta $ are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity $k$ , then the value of $4\sin \frac{\alpha }{2} + 3\sin \frac{\beta }{2} + 2\sin \frac{\gamma }{2} + \sin \frac{\delta }{2}$ is equal to
The number of values of $\alpha $ in $[0, 2\pi]$ for which $2\,{\sin ^3}\,\alpha - 7\,{\sin ^2}\,\alpha + 7\,\sin \,\alpha = 2$ , is
If $sin\, \theta = sin\, \alpha$ then $sin\, \frac{\theta }{3}$ =
If $cosx + secx =\, -2$, then for a $+ve$ integer $n$, $cos^n x + sec^n x$ is