If $\sin \theta + \operatorname{cosec} \theta = 2$,then the value of $\sin^{10} \theta + \operatorname{cosec}^{10} \theta$ is equal to

If the equation $\tan^4x - 2\sec^2x + [a]^2 = 0$ has at least one solution,then the complete range of $a$ (where $a \in R$) is:
(Note: $[k]$ denotes the greatest integer less than or equal to $k$)

Let $E = \left( 1 - \frac{\cos 61^\circ}{\cos 1^\circ} \right) \left( 1 - \frac{\cos 62^\circ}{\cos 2^\circ} \right) \dots \left( 1 - \frac{\cos 119^\circ}{\cos 59^\circ} \right)$,then $E$ is equal to:

The value of $\cos ^2 76^{\circ}+\cos ^2 16^{\circ}-\cos 76^{\circ} \cos 16^{\circ}$ is equal to

If $\tan A = 2\tan B + \cot B,$ then $2\tan (A - B) = $

The value of $\sqrt{3} \, \text{cosec} \, 20^\circ - \text{sec} \, 20^\circ$ is: