If $\frac{3\pi}{4} < \alpha < \pi,$ then $\sqrt{\csc^2 \alpha + 2\cot \alpha}$ is equal to

If $\operatorname{cosec} \theta + \cot \theta = 5$, then $\sin \theta = $

$16 \sin(20^{\circ}) \sin(40^{\circ}) \sin(80^{\circ})$ is equal to

The value of $\cos(18^{\circ}-A) \cdot \cos(18^{\circ}+A) - \cos(72^{\circ}-A) \cdot \cos(72^{\circ}+A)$ is:

If $\frac{\sin ^4 x}{2}+\frac{\cos ^4 x}{3}=\frac{1}{5},$ then
$(A) \tan ^2 x=\frac{2}{3}$ $(B) \frac{\sin ^8 x}{8}+\frac{\cos ^8 x}{27}=\frac{1}{125}$
$(C) \tan ^2 x=\frac{1}{3}$ $(D) \frac{\sin ^8 x}{8}+\frac{\cos ^8 x}{27}=\frac{2}{125}$

$\operatorname{cosec} 48^{\circ}+\operatorname{cosec} 96^{\circ}+\operatorname{cosec} 192^{\circ}+\operatorname{cosec} 384^{\circ} = $