If $\frac{{5\pi }}{2} < x < 3\pi $, then the value of the expression $\frac{{\sqrt {1 - \sin x} + \sqrt {1 + \sin x} }}{{\sqrt {1 - \sin x} - \sqrt {1 + \sin x} }}$ is
$-cot \frac{x}{2}$
$cot \frac{x}{2}$
$ tan \frac{x}{2}$
$-tan \frac{x}{2}$
If $\sin A + \cos A = \sqrt 2 ,$ then ${\cos ^2}A = $
The value of $\tan 9^{\circ}-\tan 27^{\circ}-\tan 63^{\circ}+\tan 81^{\circ}$ is $............$.
If $3\cos \theta + 4\sin \theta = 5$ then $3\sin \theta - 4\cos \theta $ is
Prove that $\sin 2 x+2 \sin 4 x+\sin 6 x=4 \cos ^{2} x \sin 4 x$
If $A, B, C$ are angles of a triangle, then $\sin 2A + \sin 2B - \sin 2C$ is equal to