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

यदि $\tan \alpha = \frac{1}{7},\;\tan \beta = \frac{1}{3},$ तब  $\cos 2\alpha = $

यदि $\sin \alpha = \frac{{336}}{{625}}$ तथा $450^\circ < \alpha < 540^\circ ,$ हो तो $\sin \left( {\frac{\alpha }{4}} \right)   $ बराबर है 

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

$\cos ^{3}\left(\frac{\pi}{8}\right) \cdot \cos \left(\frac{3 \pi}{8}\right)+\sin ^{3}\left(\frac{\pi}{8}\right) \cdot \sin \left(\frac{3 \pi}{8}\right) \text { का मान }$ है

$\sqrt 2  + \sqrt 3  + \sqrt 4  + \sqrt 6  = $