If $\frac{{\tan 3\theta - 1}}{{\tan 3\theta + 1}} = \sqrt 3 $, then the general value of $\theta $ is
$\frac{{n\pi }}{3} + \frac{\pi }{{12}}$
$\frac{{n\pi }}{3} + \frac{{7\pi }}{{36}}$
$n\pi + \frac{{7\pi }}{{12}}$
$n\pi + \frac{\pi }{{12}}$
The solution of equation ${\cos ^2}\theta + \sin \theta + 1 = 0$ lies in the interval
If $\cos 2\theta + 3\cos \theta = 0$, then the general value of $\theta $ is
One root of the equation $\cos x - x + \frac{1}{2} = 0$ lies in the interval
The set of values of $‘a’$ for which the equation, $cos\, 2x + a\, sin\, x = 2a - 7$ possess a solution is :
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 :