The value of $\sin \frac{\pi }{{14}}\sin \frac{{3\pi }}{{14}}\sin \frac{{5\pi }}{{14}}\sin \frac{{7\pi }}{{14}}\sin \frac{{9\pi }}{{14}}\sin \frac{{11\pi }}{{14}}\sin \frac{{13\pi }}{{14}}$ is equal to
$\frac{1}{8}$
$\frac{1}{{16}}$
$\frac{1}{{32}}$
$\frac{1}{{64}}$
$\frac{{\tan A + \sec A - 1}}{{\tan A - \sec A + 1}} = $
The value of the expression $(sinx + cosecx)^2 + (cosx + secx)^2 - ( tanx + cotx)^2$ wherever defined is equal to
$\tan {3^o} + 2\tan {6^o} + 4\tan {12^o} + 8\cot {24^o} = \cot {\theta ^o}$ then
If $\tan x = \frac{b}{a},$ then $\sqrt {\frac{{a + b}}{{a - b}}} + \sqrt {\frac{{a - b}}{{a + b}}} = $
If $A + B + C = \frac{\pi }{2}$ ,then value of $tanA\,\, tanB + tanB\,\, tanC + tanC\,\, tanA$ is