The expression $\tan 9^{\circ}-\tan 27^{\circ}-\tan 63^{\circ}+\tan 81^{\circ}$ is equal to

$\sec {50^o} + \tan {50^o}$ is equal to

The value of $\text{cosec}10^{\circ} - \sqrt{3} \text{sec}10^{\circ}$ is equal to:

If $\frac{\cos (A+B)}{\cos (A-B)}=\frac{\sin (C+D)}{\sin (C-D)}$,then $\tan A \tan B \tan C=$

If $\alpha, \beta$ are acute angles such that $\frac{\sin \alpha}{\sin \beta} = \frac{6}{5}$ and $\frac{\cos \alpha}{\cos \beta} = \frac{9}{5 \sqrt{5}}$,then $\sin \alpha = $

If $x=\log _e\left[\cot \left(\frac{\pi}{4}+\theta\right)\right]$ and $\theta \in\left(\frac{-\pi}{4}, \frac{\pi}{4}\right)$,then consider the following statements:
$I$ : $\cosh x=\sec 2 \theta$
$II$ : $\sinh x=-\tan 2 \theta$
Then which one of the following options is true?