यदि $\tan A = \frac{1}{2},\tan B = \frac{1}{3},$ तब $\cos 2A = $

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

यदि $\frac{x}{{\cos \theta }} = \frac{y}{{\cos \left( {\theta - \frac{{2\pi }}{3}} \right)}} = \frac{z}{{\cos \left( {\theta + \frac{{2\pi }}{3}} \right)}},$ तो $x + y + z = $

किसी त्रिभुज  $ABC$ में,  ${\sin ^2}\frac{A}{2} + {\sin ^2}\frac{B}{2} + {\sin ^2}\frac{C}{2}$ का मान होगा

$\tan 5x\tan 3x\tan 2x = $

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