$\operatorname{cosec} 40^{\circ} = \ldots \ldots \ldots \ldots$

Show that $\tan ^{4} \theta+\tan ^{2} \theta=\sec ^{4} \theta-\sec ^{2} \theta$

The value of $\tan 5^{\circ} \cdot \tan 25^{\circ} \cdot \tan 45^{\circ} \cdot \tan 65^{\circ} \cdot \tan 85^{\circ}$ is $\ldots \ldots \ldots \ldots .$.

Write 'True' or 'False' and justify your answer.
The value of $2 \sin \theta$ can be $(a + \frac{1}{a}),$ where $a$ is a positive number,and $a \neq 1$.

Show that $\frac{\cos ^{2}\left(45^{\circ}+\theta\right)+\cos ^{2}\left(45^{\circ}-\theta\right)}{\tan \left(60^{\circ}+\theta\right) \tan \left(30^{\circ}-\theta\right)}=1$

If $\sec ^{2} \theta+\tan ^{2} \theta=\frac{13}{12}$,then the value of $\sec ^{4} \theta-\tan ^{4} \theta$ is .........