If $\sin A + \sin^2 A = 1$,then the value of $\cos^2 A + \cos^4 A$ is

If $\cot \theta + \cos \theta = p$ and $\cot \theta - \cos \theta = q$,then $(p^2 - q^2)^2$ in terms of $p$ and $q$ is: (in $pq$)

Let $A, B$ and $C$ be the angles of a plane triangle and $\tan \frac{A}{2} = \frac{1}{3}, \tan \frac{B}{2} = \frac{2}{3}$. Then $\tan \frac{C}{2}$ is equal to

If $x \sin \theta = y \sin \left( \theta + \frac{2\pi}{3} \right) = z \sin \left( \theta + \frac{4\pi}{3} \right)$,then:

The angle of elevation of the top of a vertical tower situated perpendicularly on a plane is observed as $60^{\circ}$ from a point $P$ on the same plane. From another point $Q$,$10\, m$ vertically above the point $P$,the angle of depression of the foot of the tower is $30^{\circ}$. The height of the tower is (in $m$)

If $\sin x + \csc x = 2$,then $\sin^n x + \csc^n x$ is equal to