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 angles $\alpha, \beta, \gamma$ of a triangle satisfy the equations $2 \sin \alpha+3 \cos \beta=3 \sqrt{2}$ and $3 \sin \beta+2 \cos \alpha=1$. Then, angle $\gamma$ equals
All the pairs $(x, y)$ that satisfy the inequality ${2^{\sqrt {{{\sin }^2}{\kern 1pt} x - 2\sin {\kern 1pt} x + 5} }}.\frac{1}{{{4^{{{\sin }^2}\,y}}}} \leq 1$ also Satisfy the equation
The sum of solutions of the equation $\frac{\cos \mathrm{x}}{1+\sin \mathrm{x}}=|\tan 2 \mathrm{x}|, \mathrm{x} \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)-\left\{\frac{\pi}{4},-\frac{\pi}{4}\right\}$ 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
If $\cot \theta + \cot \left( {\frac{\pi }{4} + \theta } \right) = 2$, then the general value of $\theta $ is