If $\cos A = \cos B\,\,\cos C$and $A + B + C = \pi ,$ then the value of $\cot \,B\,\cot \,C$ is

$\cos \frac{{2\pi }}{{15}}\cos \frac{{4\pi }}{{15}}\cos \frac{{8\pi }}{{15}}\cos \frac{{16\pi }}{{15}}  =$

The value of $sin\,10^o$ $sin\,30^o$ $sin\,50^o$ $sin\,70^o$ is

If $A$ lies in the third quadrant and $3\,\tan A - 4 = 0,$ then $5\,\sin 2A + 3\,\sin A + 4\,\cos A = $

If $cos A = {3\over 4} , $ then $32\sin \left( {\frac{A}{2}} \right)\sin \left( {\frac{{5A}}{2}} \right) = $

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