The value of $\cot \frac{\pi}{24}$ is :
$\sqrt{2}-\sqrt{3}-2+\sqrt{6}$
$3 \sqrt{2}-\sqrt{3}-\sqrt{6}$
$\sqrt{2}-\sqrt{3}+2-\sqrt{6}$
$\sqrt{2}+\sqrt{3}+2+\sqrt{6}$
If $\sin \theta = - \frac{1}{{\sqrt 2 }}$ and $\tan \theta = 1,$ then $\theta $ lies in which quadrant
If ${\rm{cosec }}A + \cot A = \frac{{11}}{2},$ then $\tan A = $
If $\sin \theta = \frac{{ - 4}}{5}$ and $\theta $ lies in the third quadrant, then $\cos \frac{\theta }{2} = $
If $\cos \theta = \frac{1}{2}\left( {x + \frac{1}{x}} \right)$, then $\frac{1}{2}\left( {{x^2} + \frac{1}{{{x^2}}}} \right) = $
If $\sin (\alpha - \beta ) = \frac{1}{2}$ and $\cos (\alpha + \beta ) = \frac{1}{2},$ where $\alpha $ and $\beta $ are positive acute angles, then