$\tan 5x - \tan 3x - \tan 2x$ is equal to

If $x = \sec \theta + \tan \theta ,$ then $x + \frac{1}{x} = $

$\left( \frac{\sin 2A}{1 + \cos 2A} \right) \left( \frac{\cos A}{1 + \cos A} \right) = $

If $(1 + \sin A)(1 + \sin B)(1 + \sin C) = (1 - \sin A)(1 - \sin B)(1 - \sin C)$,then each side is equal to

If $\sin A = n \sin B,$ then $\frac{n - 1}{n + 1} \tan \frac{A + B}{2} = $

If $\cos \alpha = \frac{2 \cos \beta - 1}{2 - \cos \beta}$,then the value of $\tan \frac{\alpha}{2} \cot \frac{\beta}{2}$ is,where $(0 < \alpha < \pi$ and $0 < \beta < \pi$).