If $\sin \theta + \sin 2\theta + \sin 3\theta = \sin \alpha$ and $\cos \theta + \cos 2\theta + \cos 3\theta = \cos \alpha$,then $\theta$ is equal to

${\left( {\frac{{\cos A + \cos B}}{{\sin A - \sin B}}} \right)^n} + {\left( {\frac{{\sin A + \sin B}}{{\cos A - \cos B}}} \right)^n}$ ($n$ is even or odd) $=$

If $\sec \theta + \tan \theta = p, (p \neq 0)$,then $\sec \theta$ is equal to:

$\frac{\sec 8\theta - 1}{\sec 4\theta - 1}$ is equal to

From two points,lying on the same horizontal line,the angles of elevation of the top of the pillar are $\theta$ and $\phi$ $(\theta < \phi)$. If the height of the pillar is $h$ $m$ and the two points lie on the same side of the pillar,then the distance between the two points is (in $m$):

The value of $\cos (270^\circ + \theta )\,\cos (90^\circ - \theta ) - \sin (270^\circ - \theta )\,\cos \theta $ is