The value of $\cos \,\frac{\pi }{7}\,\cos \,\frac{{2\pi }}{7}\,\cos \,\frac{{3\pi }}{7}$ is

$\cos 20^\circ \cos 40^\circ \cos 80^\circ = $

If ${\rm{cosec}}\theta = \frac{{p + q}}{{p - q}},$ then $\cot \,\left( {\frac{\pi }{4} + \frac{\theta }{2}} \right) = $

Prove that: $\cos 4 x=1-8 \sin ^{2} x \cos ^{2} x$

$\frac{{\sin {{81}^o} + \cos {{81}^o}}}{{\sin {{81}^o} - \cos {{81}^o}}}$ is equal to

$\sqrt 2 + \sqrt 3 + \sqrt 4 + \sqrt 6 $ is equal to