If $\tan A = \frac{5}{6}$ and $\tan B = \frac{1}{11}$,then $A + B = $

$\frac{\sin(B + A) + \cos(B - A)}{\sin(B - A) + \cos(B + A)} = $

$\frac{\sin A+\sin 7 A+\sin 13 A}{\cos A+\cos 7 A+\cos 13 A} =$

For $\alpha, \beta \in \left(0, \frac{\pi}{2}\right)$,let $3 \sin (\alpha+\beta)=2 \sin (\alpha-\beta)$ and a real number $k$ be such that $\tan \alpha=k \tan \beta$. Then the value of $k$ is equal to :

If $\cot \alpha = 1$ and $\sec \beta = -\frac{5}{3}$,where $\pi < \alpha < \frac{3\pi}{2}$ and $\frac{\pi}{2} < \beta < \pi$,then the value of $\tan(\alpha + \beta)$ and the quadrant in which $\alpha + \beta$ lies,respectively,are

If $b \sin \alpha = a \sin (\alpha + 2\beta)$,then $\frac{a + b}{a - b} = $