$\sin \frac{\pi }{{14}}\sin \frac{{3\pi }}{{14}}\sin \frac{{5\pi }}{{14}}\sin \frac{{7\pi }}{{14}}\sin \frac{{9\pi }}{{14}}\sin \frac{{11\pi }}{{14}}\sin \frac{{13\pi }}{{14}}  = . . . .$

જો ${\cos ^6}\alpha + {\sin ^6}\alpha + K\,{\sin ^2}2\alpha = 1,$ તો $K =$

$\tan 20^\circ \tan 40^\circ \tan 60^\circ \tan 80^\circ = $

જો $x\, sin \theta = y\, sin \, \left( {\theta \,\, + \,\,\frac{{2\,\pi }}{3}} \right) = z\, sin \, \left( {\theta \,\, + \,\,\frac{{4\,\pi }}{3}} \right)$ હોય તો 

$\sqrt 2 + \sqrt 3 + \sqrt 4 + \sqrt 6 = . . ..$

$\frac{{\sin {{81}^o} + \cos {{81}^o}}}{{\sin {{81}^o} - \cos {{81}^o}}}$=