જો $\alpha + \beta = \frac{\pi }{2}$ અને $\beta + \gamma = \alpha ,$ તો  $\tan \,\alpha $ મેળવો.

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

સાબિત કરો કે : $\cos ^{2} 2 x-\cos ^{2} 6 x=\sin 4 x \sin 8 x$

જો $\alpha ,\,\beta ,\,\gamma \in \,\left( {0,\,\frac{\pi }{2}} \right)$, તો $\frac{{\sin \,(\alpha + \beta + \gamma )}}{{\sin \alpha + \sin \beta + \sin \gamma }}  = . . ..$

જો $2\sec 2\alpha = \tan \beta + \cot \beta ,$ તો $\alpha + \beta   =. . . .$

જો $A + B + C = {180^o},$ તો $\frac{{\sin 2A + \sin 2B + \sin 2C}}{{\cos A + \cos B + \cos C - 1}} = $