If $\tan A + \tan B = x$ and $\cot A + \cot B = y$,then $\tan (A + B) =$

$\cos(36^{\circ}-A) \cos(36^{\circ}+A) + \cos(54^{\circ}+A) \cos(54^{\circ}-A) = $

If $2 \sin \left(\theta+\frac{\pi}{3}\right)=\cos \left(\theta-\frac{\pi}{6}\right)$,then $\tan \theta=$

If $\sin A + \sin B = C$ and $\cos A + \cos B = D$,then the value of $\sin (A + B)$ is:

If $\frac{1-\tan \theta}{1+\tan \theta}=\frac{1}{\sqrt{3}}$,where $\theta \in \left(0, \frac{\pi}{2}\right)$,then $\theta=$

If $A$ does not belong to the first quadrant,$B$ does not belong to the second quadrant,$\sin A = \frac{11}{61}$ and $\cos B = \frac{-7}{25}$,then $A-B$ and $A+B$ lie respectively in the quadrants: