If $\frac{\sin(x+y)}{\sin(x-y)} = \frac{a+b}{a-b}$,then $\frac{\tan x}{\tan y} = $

If $\cos (A - B) = \frac{3}{5}$ and $\tan A \tan B = 2$,then

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

$\frac{\sin^2 A - \sin^2 B}{\sin A \cos A - \sin B \cos B} = $

If $\sin A = \frac{4}{5}$ and $\cos B = -\frac{12}{13}$,where $A$ and $B$ lie in the first and third quadrant respectively,then $\cos(A + B) = $

If $(1 + \tan \theta )(1 + \tan \phi ) = 2$,then $\theta + \phi = \dots ^\circ$