If $A + B + C = {180^o},$ then $\frac{{\tan A + \tan B + \tan C}}{{\tan A\,.\,\tan B\,.\,\tan C}} = $
$0$
$2$
$1$
$-1$
If $\sin A = n\sin B,$ then $\frac{{n - 1}}{{n + 1}}\tan \,\frac{{A + B}}{2} = $
If ${\cos ^6}\alpha + {\sin ^6}\alpha + K\,{\sin ^2}2\alpha = 1,$ then $K =$
$\sin 4\theta $ can be written as
$\sin 12^\circ \sin 48^\circ \sin 54^\circ = $
The value of $\cos \,\frac{\pi }{7}\,\cos \,\frac{{2\pi }}{7}\,\cos \,\frac{{3\pi }}{7}$ is