If $\tan A = \frac{1}{2},$ then $\tan 3A = $
$\frac{9}{2}$
$\frac{{11}}{2}$
$\frac{7}{2}$
$ - \frac{1}{2}$
If $A, B, C$ are acute positive angles such that $A + B + C = \pi $ and $\cot A\,\cot \,B\,\cot \,C = K,$ then
If $A + B + C = {180^o},$ then the value of $(\cot B + \cot C)$ $(\cot C + \cot A)\,\,(\cot A + \cot B)$ will be
The value of $\tan 7\frac{1}{2}^\circ $ is equal to
Let $\alpha ,\beta $ be such that $\pi < (\alpha - \beta ) < 3\pi $. If $\sin \alpha + \sin \beta = - \frac{{21}}{{65}}$ and $\cos \alpha + \cos \beta = - \frac{{27}}{{65}},$ then the value of $\cos \frac{{\alpha - \beta }}{2}$ is
$\frac{{\sec \,8\theta - 1}}{{\sec \,4\theta - 1}}$ is equal to