$\left(0, \frac{\pi}{2}\right)$

$\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$

$\left(-\frac{3 \pi}{4}, \frac{\pi}{4}\right)$

$\left(\frac{\pi}{4}, \frac{\pi}{2}\right)$

$\left(0, \frac{\pi}{4}\right]$

$\left[\frac{\pi}{4}, \frac{\pi}{2}\right)$

$[0, \pi]$

$\left[\frac{\pi}{6}, \frac{\pi}{2}\right)$

$(-1,2)$

$(1, \infty)$

$(-\infty, \infty)$

$(-\infty, 1)$

$\log \left(\sin \alpha+\sqrt{\sin ^2 \alpha-1}\right)$

$\log (\tan \alpha+1)$

$\log \left(\cot \frac{\alpha}{2}\right)$

$\log \left(\frac{1+\tan \alpha}{2 \sin \alpha}\right)$