જો $\alpha ,\,\beta ,\,\gamma \in \,\left( {0,\,\frac{\pi }{2}} \right)$, તો $\frac{{\sin \,(\alpha + \beta + \gamma )}}{{\sin \alpha + \sin \beta + \sin \gamma }}  = . . ..$

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

$\frac{{\tan \,\,\left( {x\,\, - \,\,{\textstyle{\pi  \over 2}}} \right)\,\,.\,\,\cos \,\,\left( {{\textstyle{{3\pi } \over 2}}\,\, + \,\,x} \right)\,\, - \,\,{{\sin }^3}\,\left( {{\textstyle{{7\pi } \over 2}}\,\, - \,\,x} \right)}}{{\cos \,\,\left( {x\,\, - \,\,{\textstyle{\pi  \over 2}}} \right)\,\,.\,\,\tan \,\,\left( {{\textstyle{{3\pi } \over 2}}\,\, + \,\,x} \right)}}$  = 

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

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

$(\sec 2A + 1){\sec ^2}A = $