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

Which of the following relations is correct for $0^{\circ} < \theta < 90^{\circ}$?

If $180^{\circ} < \theta < 270^{\circ},$ then the value of $\sqrt{4 \sin^{4} \theta + \sin^{2} 2\theta} + 4 \cos^{2} \left(\frac{\pi}{4} - \frac{\theta}{2}\right)$ is

The value of $\frac{\cos 2 \theta}{1-\sin 2 \theta}=$

The value of $\cos 41^{\circ} \cdot \cos 42^{\circ} \cdot \cos 43^{\circ} \cdot \cos 44^{\circ} \cdot \cos 45^{\circ} \cdot \cos 46^{\circ} \cdot \cos 47^{\circ} \cdot \cos 48^{\circ} \cdot \cos 49^{\circ}$ is:

If $\log_a b + \log_b c + \log_c a$ vanishes,where $a, b,$ and $c$ are positive real numbers different from unity,then the value of $(\log_a b)^3 + (\log_b c)^3 + (\log_c a)^3$ is