$(-1,2)$

$(1, \infty)$

$(-\infty, \infty)$

$(-\infty, 1)$

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

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

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

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

1

3

$\frac{1}{2}$

$\frac{3}{2}$

$-\frac{\left|\operatorname{cosec} \frac{x}{2}\right|}{2 \sqrt{\sin ^2 \frac{x}{2}-\cos ^2 \frac{x}{2}}}$

$\frac{\left|\sec \frac{x}{2}\right|}{2 \sqrt{\cos x}}$

$\frac{\cos \frac{x}{2}}{2 \sqrt{\cos x}}$

$\frac{\cos \frac{x}{2}}{\sqrt{\cos x}}$