$3\,\left[ {{{\sin }^4}\,\left( {\frac{{3\pi }}{2} - \alpha } \right) + {{\sin }^4}\,(3\pi + \alpha )} \right]$ $ - 2\,\left[ {{{\sin }^6}\,\left( {\frac{\pi }{2} + \alpha } \right) + {{\sin }^6}(5\pi - \alpha )} \right] = $

$\frac{{\cos A}}{{1 - \sin A}} = $

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

यदि $\sin \theta  + \sin 2\theta  + \sin 3\theta  = \sin \alpha $ तथा $\cos \theta  + \cos 2\theta  + \cos 3\theta  = \cos \alpha $, तब $\theta$  का मान होगा

यदि $\sin \alpha = \frac{{ - 3}}{5},$ जहाँ  $\pi < \alpha < \frac{{3\pi }}{2},$ तो $\cos \frac{1}{2}\alpha = $

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