If $A + B + C = {180^o},$ then $\frac{{\sin 2A + \sin 2B + \sin 2C}}{{\cos A + \cos B + \cos C - 1}} = $
$8\,\sin \frac{A}{2}\sin \frac{B}{2}\sin \frac{C}{2}$
$8\cos \frac{A}{2}\cos \frac{B}{2}\cos \frac{C}{2}$
$8\,\sin \frac{A}{2}\cos \frac{B}{2}\cos \frac{C}{2}$
$8\,\cos \frac{A}{2}\sin \frac{B}{2}\sin \frac{C}{2}$
$4 \,\,sin5^o \,\,sin55^o \,\,sin65^o$ has the values equal to
$\frac{{\sin 3\theta - \cos 3\theta }}{{\sin \theta + \cos \theta }} + 1 = $
If $\cos \theta = \frac{1}{2}\left( {a + \frac{1}{a}} \right),$then the value of $\cos 3\theta $is
If $a\,\cos 2\theta + b\,\sin 2\theta = c$ has $\alpha$ and $\beta$ as its solution, then the value of $\tan \alpha + \tan \beta $ is
The sum of all values of $\theta \, \in \,\left( {0,\frac{\pi }{2}} \right)$ satisfying ${\sin ^2}\,2\theta + {\cos ^4}\,2\theta = \frac{3}{4}$ is