If $\tan (A-B) = \frac{7}{24}$ and $\tan A = \frac{4}{3}$,where $A$ and $B$ are acute,then $A+B = $

If $x=a(\sin \theta+\cos \theta)$ and $y=b(\sin \theta-\cos \theta)$,then the value of $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}$ is

If $180^{\circ} < \theta < 270^{\circ},$ then the value of $\sqrt{4 \sin^{4} \theta + \sin^{2} 2\theta} + 4 \cos^{2} \left(\frac{\pi}{4} - \frac{\theta}{2}\right)$ is

If $\sin \theta + \sin \phi = a$ and $\cos \theta + \cos \phi = b,$ then $\tan \frac{\theta - \phi}{2}$ is equal to

$\frac{{\cot^2 15^\circ - 1}}{{\cot^2 15^\circ + 1}} = $

If $\frac{\pi}{2} < \alpha < \pi$ and $\pi < \beta < \frac{3\pi}{2}$,with $\sin \alpha = \frac{15}{17}$ and $\tan \beta = \frac{12}{5}$,then the value of $\sin(\beta - \alpha)$ is: (in $/221$)