If $\cot \theta + \tan \theta = 2{\rm{cosec}}\theta $, the general value of $\theta $ is
$n\pi \pm \frac{\pi }{3}$
$n\pi \pm \frac{\pi }{6}$
$2n\pi \pm \frac{\pi }{3}$
$2n\pi \pm \frac{\pi }{6}$
If $\frac{{1 - {{\tan }^2}\theta }}{{{{\sec }^2}\theta }} = \frac{1}{2}$, then the general value of $\theta $ is
If $\frac{{\tan 3\theta - 1}}{{\tan 3\theta + 1}} = \sqrt 3 $, then the general value of $\theta $ is
The general value of $\theta $ in the equation $2\sqrt 3 \cos \theta = \tan \theta $, is
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 solution of $3\tan (A - {15^o}) = \tan (A + {15^o})$ is