જો $a\tan \theta = b$, તો $a\cos 2\theta + b\sin 2\theta = $

$\frac{1}{4} \,\,tan \frac{\pi}{8} +\frac{1}{8} \,\,tan \frac{\pi}{16}+\frac{1}{16} \,\,tan \frac{\pi}{32}+.\,.\,.\,\infty  $ પદ =

જો $\tan \alpha = \frac{1}{7}$ અને $\sin \beta = \frac{1}{{\sqrt {10} }}\left( {0 < \alpha ,\,\beta < \frac{\pi }{2}} \right)$, તો $2\beta  = . . . .$

 $\left( {1 + \cos \frac{\pi }{9}} \right)\left( {1 + \cos \frac{{3\pi }}{9}} \right)\left( {1 + \cos \frac{{5\pi }}{9}} \right)\left( {1 + \cos \frac{{7\pi }}{9}} \right)$ની કિમત ............ થાય 

$\tan \frac{A}{2} = . . .$

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 = $