$\frac{\cos 12^\circ - \sin 12^\circ}{\cos 12^\circ + \sin 12^\circ} + \frac{\sin 147^\circ}{\cos 147^\circ} = $

If $\cos A = -\frac{60}{61}$ and $\tan B = -\frac{7}{24}$ and neither $A$ nor $B$ is in the second quadrant,then the angle $A + \frac{B}{2}$ lies in the quadrant:

$16 \sin(20^{\circ}) \sin(40^{\circ}) \sin(80^{\circ})$ is equal to

The value of $\tan 40^{\circ} + \tan 11^{\circ} + \tan 20^{\circ} - \tan 56^{\circ} + \tan 56^{\circ} \tan 11^{\circ} + \sqrt{3} \tan 40^{\circ} \tan 20^{\circ}$ is

If $\sin x+\sin ^2 x=1$,where $x \in\left(0, \frac{\pi}{2}\right)$,then the value of $(\cos ^{12} x+\tan ^{12} x)+3(\cos ^{10} x+\tan ^{10} x+\cos ^8 x+\tan ^8 x)+(\cos ^6 x+\tan ^6 x)$ is equal to

If $\sin A = n \sin (A + 2B)$,then $\tan (A + B) =$