The general value of $\theta $ that satisfies both the equations $cot^3\theta + 3 \sqrt 3 $ = $0$ & $cosec^5\theta + 32$ = $0$ is $(n \in I)$
$2n\pi - \frac{\pi }{6}$
$n\pi - \frac{\pi }{6}$
$n\pi - {\left( { - 1} \right)^n}\frac{\pi }{6}$
$n\pi + \frac{\pi }{3}$
If $e ^{\left(\cos ^{2} x+\cos ^{4} x+\cos ^{6} x+\ldots \ldots \infty\right) \log _{e} 2}$ satisfies the equation $t ^{2}-9 t +8=0,$ then the value of $\frac{2 \sin x}{\sin x+\sqrt{3} \cos x}\left(0 < x < \frac{\pi}{2}\right)$ is
For $n \in Z$ , the general solution of the equation
$(\sqrt 3 - 1)\,\sin \,\theta \, + \,(\sqrt 3 + 1)\,\cos \theta \, = \,2$ is
Solve $\sin 2 x-\sin 4 x+\sin 6 x=0$
All possible values of $\theta \in[0,2 \pi]$ for which $\sin 2 \theta+\tan 2 \theta>0$ lie in
The value of the expression
$\frac{{\left (sin 36^o + cos 36^o - \sqrt 2 sin 27^o)( {\sin {{36}^0} + \cos {{36}^0} - \sqrt 2 \sin {{27}^0}} \right)}}{{2\sin {{54}^0}}}$ is less than