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 $/221$)

$\frac{\sec 8A - 1}{\sec 4A - 1} = $

The value of $\tan^{-1} \left( \frac{\sin 2 - 1}{\cos 2} \right)$ is equal to:

The numerical value of $\frac{\cos ^{2} 45^{\circ}}{\sin ^{2} 60^{\circ}}+\frac{\cos ^{2} 60^{\circ}}{\sin ^{2} 45^{\circ}}-\frac{\tan ^{2} 30^{\circ}}{\cot ^{2} 45^{\circ}}-\frac{\sin ^{2} 30^{\circ}}{\cot ^{2} 30^{\circ}}$ is

If $\theta+\phi=\frac{2 \pi}{3}$ and $\cos \theta=\frac{\sqrt{3}}{2},$ what is the value of $\sin \phi ?$

If $x \cos \theta - \sin \theta = 1$,then $x^2 - (1 + x^2) \sin \theta$ equals