In triangle $ABC$, the value of $\sin 2A + \sin 2B + \sin 2C$ is equal to
$4\sin A.\,\sin B.\,\sin C$
$4\cos A.\,\cos B.\,\cos C$
$2\cos A.\,\cos B.\,\cos C$
$2\sin A.\,\sin B.\,\,\sin C$
If $\sin \alpha = \frac{{ - 3}}{5},$ where $\pi < \alpha < \frac{{3\pi }}{2},$ then $\cos \frac{1}{2}\alpha = $
If $\tan x + \tan \left( {\frac{\pi }{3} + x} \right) + \tan \left( {\frac{{2\pi }}{3} + x} \right) = 3,$ then
If $\sin \theta + \sin 2\theta + \sin 3\theta = \sin \alpha $and $\cos \theta + \cos 2\theta + \cos 3\theta = \cos \alpha $, then $\theta$ is equal to
If $\cos \theta = \frac{1}{2}\left( {a + \frac{1}{a}} \right),$then the value of $\cos 3\theta $is
If $2\sec 2\alpha = \tan \beta + \cot \beta ,$ then one of the values of $\alpha + \beta $ is