$\sin 5^{\circ} + \sin 10^{\circ} + \sin 15^{\circ} + \dots + \sin 350^{\circ} + \sin 355^{\circ}$ is equal to:

In a $\Delta ABC$,if the median,bisector,and altitude drawn from the vertex $A$ divide the angle at the vertex into four equal parts,then the angles of the $\Delta ABC$ are:

If $\sin \theta + \cos \theta = m$ and $\sec \theta + \text{cosec} \theta = n$,then $n(m + 1)(m - 1) = $

The number of all possible values of $\theta$,where $0 < \theta < \pi$,for which the system of equations
$(y+z) \cos 3\theta = (xyz) \sin 3\theta$
$x \sin 3\theta = \frac{2 \cos 3\theta}{y} + \frac{2 \sin 3\theta}{z}$
$(xyz) \sin 3\theta = (y+2z) \cos 3\theta + y \sin 3\theta$
have a solution $(x_0, y_0, z_0)$ with $y_0 z_0 \neq 0$,is

If $A$ and $B$ are acute angles such that $\sin A = \sin^2 B$ and $2 \cos^2 A = 3 \cos^2 B$, then $(A, B) =$

If $\frac{\cos x}{\cos (x-2 y)}=\lambda$,then $\tan (x-y) \tan y$ is equal to