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

If $A + B + C = {180^o},$ then $\frac{{\tan A + \tan B + \tan C}}{{\tan A\,.\,\tan B\,.\,\tan C}} = $

Let $A, B, C$ are three angles such that $sinA + sinB + sinC = 0,$ then

$ \frac {sinAsin BsinC}{(sin 3A+ sin 3B+ sin 3C)}$ (wherever definied) is -

$\frac{{\cos 12^\circ - \sin 12^\circ }}{{\cos 12^\circ + \sin 12^\circ }} + \frac{{\sin 147^\circ }}{{\cos 147^\circ }} = $

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

For any $\theta \, \in \,\left( {\frac{\pi }{4},\frac{\pi }{2}} \right)$, the expression $3\,{\left( {\sin \,\theta  - \cos \,\theta } \right)^4} + 6{\left( {\sin \,\theta  + \cos \,\theta } \right)^2} + 4\,{\sin ^6}\,\theta $ equals