જો $\tan A = \frac{1}{2},$ તો $\tan 3A = $

જો $\tan \theta = \frac{{\sin \alpha - \cos \alpha }}{{\sin \alpha + \cos \alpha }},$ તો $\sin \alpha + \cos \alpha $ અને $\sin \alpha - \cos \alpha $ ની કિમત . . . . ને સમાન થવી જ જોઈએ.

$\sqrt 3 \,{\rm{cosec}}\,{20^o} - \sec \,{20^o} = $

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

$cos^273^o  + cos^247^o  + (cos73^o  . cos47^o )$ = 

જો $A + B + C = \pi ,$ તો ${\tan ^2}\frac{A}{2} + {\tan ^2}\frac{B}{2} + $${\tan ^2}\frac{C}{2}$ એ . . ..