If $\sin \theta = \sqrt 3 \cos \theta , - \pi < \theta < 0$, then $\theta = $
$ - \frac{{5\pi }}{6}$
$ - \frac{{4\pi }}{6}$
$\frac{{4\pi }}{6}$
$\frac{{5\pi }}{6}$
If $A, B, C, D$ are the angles of a cyclic quadrilateral taken in order, then
$cos(180^o + A) + cos(180^o -B) + cos(180^o -C) -sin(90^o -D)=$
The number of solution of the equation $\tan x + \sec x = 2\cos x$ lying in the interval $(0,2\pi )$ is
If $\tan (\cot x) = \cot (\tan x),$ then $\sin 2x =$
If $\operatorname{cosec}^2(\alpha+\beta)-\sin ^2(\beta-\alpha)+\sin ^2(2 \alpha-\beta)=\cos ^2(\alpha-\beta)$ where $\alpha, \beta \in\left(0, \frac{\pi}{2}\right)$, then $\sin (\alpha-\beta)$ is equal to
Find the principal and general solutions of the equation $\cot x=-\sqrt{3}$