જો $2\tan A = 3\tan B,$ તો $\frac{{\sin 2B}}{{5 - \cos 2B}}  = . . . .$

$\left( {1 + \cos \frac{\pi }{8}} \right)\,\left( {1 + \cos \frac{{3\pi }}{8}} \right)\,\left( {1 + \cos \frac{{5\pi }}{8}} \right)\,\left( {1 + \cos \frac{{7\pi }}{8}} \right) = $

જો a $cos^3 \alpha + 3a \,cos\, \alpha \, sin^2\, \alpha = m$અને $asin^3\, \alpha + 3a \, cos^2\, \alpha \,sin\, \alpha = n$ હોય તો  $(m + n)^{2/3} + (m - n)^{2/3}$ = 

$\sin {20^o}\,\sin {40^o}\,\sin {60^o}\,\sin {80^o} = $

સમીકરણ ${\sin ^2}\,2\theta  + {\cos ^4}\,2\theta  = \frac{3}{4}$ ના $\theta \, \in \,\left( {0,\frac{\pi }{2}} \right)$ ના બધા ઉકેલો નો સરવાળો .......... થાય.

 $cot\, 7\frac{{{1^0}}}{2}$ $+ tan\, 67 \frac{{{1^0}}}{2} - cot 67 \frac{{{1^0}}}{2} - tan7 \frac{{{1^0}}}{2}$ =