If $\sin \theta + \csc \theta = 2$,then $\sin^2 \theta + \csc^2 \theta = $

The value of $\cos 41^{\circ} \cdot \cos 42^{\circ} \cdot \cos 43^{\circ} \cdot \cos 44^{\circ} \cdot \cos 45^{\circ} \cdot \cos 46^{\circ} \cdot \cos 47^{\circ} \cdot \cos 48^{\circ} \cdot \cos 49^{\circ}$ is:

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

If $\tan \theta = \frac{x \sin \phi}{1 - x \cos \phi}$ and $\tan \phi = \frac{y \sin \theta}{1 - y \cos \theta}$,then $\frac{x}{y} = $

Let $A, B, C$ be three angles such that $\sin A + \sin B + \sin C = 0$. Then,$\frac{\sin A \sin B \sin C}{\sin 3A + \sin 3B + \sin 3C}$ (wherever defined) is equal to:

If $5 \cos \theta + 12 \sin \theta = 13,$ then $\tan \theta = ?$