The sum of all values of $\theta \, \in \,\left( {0,\frac{\pi }{2}} \right)$ satisfying ${\sin ^2}\,2\theta + {\cos ^4}\,2\theta = \frac{3}{4}$ is
$\pi $
$\frac{{5\pi }}{4}$
$\frac{{\pi }}{2}$
$\frac{{3\pi }}{8}$
$\tan \frac{A}{2}$ is equal to
The value of $\tan 9^{\circ}-\tan 27^{\circ}-\tan 63^{\circ}+\tan 81^{\circ}$ is $............$.
Prove that $\cos ^{2} 2 x-\cos ^{2} 6 x=\sin 4 x \sin 8 x$
$\frac{{\sin 3\theta + \sin 5\theta + \sin 7\theta + \sin 9\theta }}{{\cos 3\theta + \cos 5\theta + \cos 7\theta + \cos 9\theta }} = $
If $90^\circ < A < 180^\circ $ and $\sin A = \frac{4}{5},$ then $\tan \frac{A}{2}$ is equal to