If $A + B + C = 180^o,$ then $\frac{\tan A + \tan B + \tan C}{\tan A \cdot \tan B \cdot \tan C} = $

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 $0 < \beta < \pi$).

$\frac{\tan ^{2} \theta}{\sec \theta+1}-\sec \theta$ is equal to

If $\sec \theta + \tan \theta = m$ $(m > 1)$,then the value of $\sin \theta$ is $(0^{\circ} < \theta < 90^{\circ})$.

If $\frac{5\pi}{2} < x < 3\pi$,then the value of the expression $\frac{\sqrt{1 - \sin x} + \sqrt{1 + \sin x}}{\sqrt{1 - \sin x} - \sqrt{1 + \sin x}}$ is

If $\sin x + \sin^2 x = 1$,then the value of $\cos^{12} x + 3\cos^{10} x + 3\cos^8 x + \cos^6 x - 2$ is equal to