If $\sin \theta = \frac{{ - 4}}{5}$ and $\theta $ lies in the third quadrant, then $\cos \frac{\theta }{2} = $
$\frac{1}{{\sqrt 5 }}$
$ - \frac{1}{{\sqrt 5 }}$
$\sqrt {\frac{2}{5}} $
$ - \sqrt {\frac{2}{5}} $
If $(1 + \sin A)(1 + \sin B)(1 + \sin C)$$ = (1 - \sin A)(1 - \sin B)(1 - \sin C),$ then each side is equal to
The equation ${\sec ^2}\theta = \frac{{4xy}}{{{{(x + y)}^2}}}$ is only possible when
If $\frac{{3\pi }}{4} < \alpha < \pi ,$ then $\sqrt {{\rm{cose}}{{\rm{c}}^2}\alpha + 2\cot \alpha } $ is equal to
$\frac{{2\sin \theta \,\tan \theta (1 - \tan \theta ) + 2\sin \theta {{\sec }^2}\theta }}{{{{(1 + \tan \theta )}^2}}} = $
The value of $\frac{{\cot 54^\circ }}{{\tan 36^\circ }} + \frac{{\tan 20^\circ }}{{\cot 70^\circ }}$ is